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2291 2296
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2323 2328
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5 37
2344 2350
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2377 2382
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5 38
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2489 2495
2500
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5 |
1 | 506-509 | 37
2344 2350
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2377 2382
2388
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5 38
2399 2404
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2432 2438
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1
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5 39
2455 2460
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2489 2495
2500
2506
1
1
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5 40
2512 2518
2523
2529
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2547 2553
2559
2564
1
1
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2
3
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4
5
5 |
1 | 507-510 | 38
2399 2404
2410
2415
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2427
2432 2438
2443
2449
1
1
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2
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3
4
4
5 39
2455 2460
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2489 2495
2500
2506
1
1
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3
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5
5 40
2512 2518
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2547 2553
2559
2564
1
1
2
2
3
4
4
5
5 41
2570 2576
2582
2588
2594
2600
2606 2612
2618
2624
1
1
2
2
3
4
4
5
5 |
1 | 508-511 | 39
2455 2460
2466
2472
2477
2483
2489 2495
2500
2506
1
1
2
2
3
3
4
5
5 40
2512 2518
2523
2529
2535
2541
2547 2553
2559
2564
1
1
2
2
3
4
4
5
5 41
2570 2576
2582
2588
2594
2600
2606 2612
2618
2624
1
1
2
2
3
4
4
5
5 42
2630 2636
2642
2649
2655
2661
2667 2673
2679
2685
1
1
2
2
3
4
4
5
6 |
1 | 509-512 | 40
2512 2518
2523
2529
2535
2541
2547 2553
2559
2564
1
1
2
2
3
4
4
5
5 41
2570 2576
2582
2588
2594
2600
2606 2612
2618
2624
1
1
2
2
3
4
4
5
5 42
2630 2636
2642
2649
2655
2661
2667 2673
2679
2685
1
1
2
2
3
4
4
5
6 43
2692 2698
2704
2710
2716
2723
2729 2735
2742
2748
1
1
2
3
3
4
4
5
6 |
1 | 510-513 | 41
2570 2576
2582
2588
2594
2600
2606 2612
2618
2624
1
1
2
2
3
4
4
5
5 42
2630 2636
2642
2649
2655
2661
2667 2673
2679
2685
1
1
2
2
3
4
4
5
6 43
2692 2698
2704
2710
2716
2723
2729 2735
2742
2748
1
1
2
3
3
4
4
5
6 44
2754 2761
2767
2773
2780
2786
2793 2799
2805
2812
1
1
2
3
3
4
4
5
6 |
1 | 511-514 | 42
2630 2636
2642
2649
2655
2661
2667 2673
2679
2685
1
1
2
2
3
4
4
5
6 43
2692 2698
2704
2710
2716
2723
2729 2735
2742
2748
1
1
2
3
3
4
4
5
6 44
2754 2761
2767
2773
2780
2786
2793 2799
2805
2812
1
1
2
3
3
4
4
5
6 45
2818 2825
2831
2838
2844
2851
2858 2864
2871
2877
1
1
2
3
3
4
5
5
6 |
1 | 512-515 | 43
2692 2698
2704
2710
2716
2723
2729 2735
2742
2748
1
1
2
3
3
4
4
5
6 44
2754 2761
2767
2773
2780
2786
2793 2799
2805
2812
1
1
2
3
3
4
4
5
6 45
2818 2825
2831
2838
2844
2851
2858 2864
2871
2877
1
1
2
3
3
4
5
5
6 46
2884 2891
2897
2904
2911
2917
2924 2931
2938
2944
1
1
2
3
3
4
5
5
6 |
1 | 513-516 | 44
2754 2761
2767
2773
2780
2786
2793 2799
2805
2812
1
1
2
3
3
4
4
5
6 45
2818 2825
2831
2838
2844
2851
2858 2864
2871
2877
1
1
2
3
3
4
5
5
6 46
2884 2891
2897
2904
2911
2917
2924 2931
2938
2944
1
1
2
3
3
4
5
5
6 47
2951 2958
2965
2972
2979
2985
2992 2999
3006
3013
1
1
2
3
3
4
5
5
6 |
1 | 514-517 | 45
2818 2825
2831
2838
2844
2851
2858 2864
2871
2877
1
1
2
3
3
4
5
5
6 46
2884 2891
2897
2904
2911
2917
2924 2931
2938
2944
1
1
2
3
3
4
5
5
6 47
2951 2958
2965
2972
2979
2985
2992 2999
3006
3013
1
1
2
3
3
4
5
5
6 48
3020 3027
3034
3041
3048
3055
3062 3069
3076
3083
1
1
2
3
3
4
5
6
6 |
1 | 515-518 | 46
2884 2891
2897
2904
2911
2917
2924 2931
2938
2944
1
1
2
3
3
4
5
5
6 47
2951 2958
2965
2972
2979
2985
2992 2999
3006
3013
1
1
2
3
3
4
5
5
6 48
3020 3027
3034
3041
3048
3055
3062 3069
3076
3083
1
1
2
3
3
4
5
6
6 49
3090 3097
3105
3112
3119
3126
3133 3141
3148
3155
1
1
2
3
3
4
5
6
6
ANTILOGARITHMS
TABLE II
Rationalised 2023-24
153
Appendix
ANTILOGARITHMS
TABLE II (Continued)
N
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9 |
1 | 516-519 | 47
2951 2958
2965
2972
2979
2985
2992 2999
3006
3013
1
1
2
3
3
4
5
5
6 48
3020 3027
3034
3041
3048
3055
3062 3069
3076
3083
1
1
2
3
3
4
5
6
6 49
3090 3097
3105
3112
3119
3126
3133 3141
3148
3155
1
1
2
3
3
4
5
6
6
ANTILOGARITHMS
TABLE II
Rationalised 2023-24
153
Appendix
ANTILOGARITHMS
TABLE II (Continued)
N
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9 50
3162 3170
3177
3184
3192
3199
3206 3214
3221
3228
1
1
2
3
4
4
5
6
7 |
1 | 517-520 | 48
3020 3027
3034
3041
3048
3055
3062 3069
3076
3083
1
1
2
3
3
4
5
6
6 49
3090 3097
3105
3112
3119
3126
3133 3141
3148
3155
1
1
2
3
3
4
5
6
6
ANTILOGARITHMS
TABLE II
Rationalised 2023-24
153
Appendix
ANTILOGARITHMS
TABLE II (Continued)
N
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9 50
3162 3170
3177
3184
3192
3199
3206 3214
3221
3228
1
1
2
3
4
4
5
6
7 51
3236 3243
3251
3258
3266
3273
3281 3289
3296
3304
1
2
2
3
4
5
5
6
7 |
1 | 518-521 | 49
3090 3097
3105
3112
3119
3126
3133 3141
3148
3155
1
1
2
3
3
4
5
6
6
ANTILOGARITHMS
TABLE II
Rationalised 2023-24
153
Appendix
ANTILOGARITHMS
TABLE II (Continued)
N
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9 50
3162 3170
3177
3184
3192
3199
3206 3214
3221
3228
1
1
2
3
4
4
5
6
7 51
3236 3243
3251
3258
3266
3273
3281 3289
3296
3304
1
2
2
3
4
5
5
6
7 52
3311 3319
3327
3334
3342
3350
3357 3365
3373
3381
1
2
2
3
4
5
5
6
7 |
1 | 519-522 | 50
3162 3170
3177
3184
3192
3199
3206 3214
3221
3228
1
1
2
3
4
4
5
6
7 51
3236 3243
3251
3258
3266
3273
3281 3289
3296
3304
1
2
2
3
4
5
5
6
7 52
3311 3319
3327
3334
3342
3350
3357 3365
3373
3381
1
2
2
3
4
5
5
6
7 53
3388 3396
3404
3412
3420
3428
3436 3443
3451
3459
1
2
2
3
4
5
6
6
7 |
1 | 520-523 | 51
3236 3243
3251
3258
3266
3273
3281 3289
3296
3304
1
2
2
3
4
5
5
6
7 52
3311 3319
3327
3334
3342
3350
3357 3365
3373
3381
1
2
2
3
4
5
5
6
7 53
3388 3396
3404
3412
3420
3428
3436 3443
3451
3459
1
2
2
3
4
5
6
6
7 54
3467 3475
3483
3491
3499
3508
3516 3524
3532
3540
1
2
2
3
4
5
6
6
7 |
1 | 521-524 | 52
3311 3319
3327
3334
3342
3350
3357 3365
3373
3381
1
2
2
3
4
5
5
6
7 53
3388 3396
3404
3412
3420
3428
3436 3443
3451
3459
1
2
2
3
4
5
6
6
7 54
3467 3475
3483
3491
3499
3508
3516 3524
3532
3540
1
2
2
3
4
5
6
6
7 55
3548 3556
3565
3573
3581
3589
3597 3606
3614
3622
1
2
2
3
4
5
6
7
7 |
1 | 522-525 | 53
3388 3396
3404
3412
3420
3428
3436 3443
3451
3459
1
2
2
3
4
5
6
6
7 54
3467 3475
3483
3491
3499
3508
3516 3524
3532
3540
1
2
2
3
4
5
6
6
7 55
3548 3556
3565
3573
3581
3589
3597 3606
3614
3622
1
2
2
3
4
5
6
7
7 56
3631 3639
3648
3656
3664
3673
3681 3690
3698
3707
1
2
3
3
4
5
6
7
8 |
1 | 523-526 | 54
3467 3475
3483
3491
3499
3508
3516 3524
3532
3540
1
2
2
3
4
5
6
6
7 55
3548 3556
3565
3573
3581
3589
3597 3606
3614
3622
1
2
2
3
4
5
6
7
7 56
3631 3639
3648
3656
3664
3673
3681 3690
3698
3707
1
2
3
3
4
5
6
7
8 57
3715 3724
3733
3741
3750
3758
3767 3776
3784
3793
1
2
3
3
4
5
6
7
8 |
1 | 524-527 | 55
3548 3556
3565
3573
3581
3589
3597 3606
3614
3622
1
2
2
3
4
5
6
7
7 56
3631 3639
3648
3656
3664
3673
3681 3690
3698
3707
1
2
3
3
4
5
6
7
8 57
3715 3724
3733
3741
3750
3758
3767 3776
3784
3793
1
2
3
3
4
5
6
7
8 58
3802 3811
3819
3828
3837
3846
3855 3864
3873
3882
1
2
3
4
4
5
6
7
8 |
1 | 525-528 | 56
3631 3639
3648
3656
3664
3673
3681 3690
3698
3707
1
2
3
3
4
5
6
7
8 57
3715 3724
3733
3741
3750
3758
3767 3776
3784
3793
1
2
3
3
4
5
6
7
8 58
3802 3811
3819
3828
3837
3846
3855 3864
3873
3882
1
2
3
4
4
5
6
7
8 59
3890 3899
3908
3917
3926
3936
3945 3954
3963
3972
1
2
3
4
5
5
6
7
8 |
1 | 526-529 | 57
3715 3724
3733
3741
3750
3758
3767 3776
3784
3793
1
2
3
3
4
5
6
7
8 58
3802 3811
3819
3828
3837
3846
3855 3864
3873
3882
1
2
3
4
4
5
6
7
8 59
3890 3899
3908
3917
3926
3936
3945 3954
3963
3972
1
2
3
4
5
5
6
7
8 60
3981 3990
3999
4009
4018
4027
4036 4046
4055
4064
1
2
3
4
5
6
6
7
8 |
1 | 527-530 | 58
3802 3811
3819
3828
3837
3846
3855 3864
3873
3882
1
2
3
4
4
5
6
7
8 59
3890 3899
3908
3917
3926
3936
3945 3954
3963
3972
1
2
3
4
5
5
6
7
8 60
3981 3990
3999
4009
4018
4027
4036 4046
4055
4064
1
2
3
4
5
6
6
7
8 61
4074 4083
4093
4102
4111
4121
4130 4140
4150
4159
1
2
3
4
5
6
7
8
9 |
1 | 528-531 | 59
3890 3899
3908
3917
3926
3936
3945 3954
3963
3972
1
2
3
4
5
5
6
7
8 60
3981 3990
3999
4009
4018
4027
4036 4046
4055
4064
1
2
3
4
5
6
6
7
8 61
4074 4083
4093
4102
4111
4121
4130 4140
4150
4159
1
2
3
4
5
6
7
8
9 62
4169 4178
4188
4198
4207
4217
4227 4236
4246
42S6
1
2
3
4
5
6
7
8
9 |
1 | 529-532 | 60
3981 3990
3999
4009
4018
4027
4036 4046
4055
4064
1
2
3
4
5
6
6
7
8 61
4074 4083
4093
4102
4111
4121
4130 4140
4150
4159
1
2
3
4
5
6
7
8
9 62
4169 4178
4188
4198
4207
4217
4227 4236
4246
42S6
1
2
3
4
5
6
7
8
9 63
4266 4276
4285
4295
4305
4315
4325 4335
4345
4355
1
2
3
4
5
6
7
8
9 |
1 | 530-533 | 61
4074 4083
4093
4102
4111
4121
4130 4140
4150
4159
1
2
3
4
5
6
7
8
9 62
4169 4178
4188
4198
4207
4217
4227 4236
4246
42S6
1
2
3
4
5
6
7
8
9 63
4266 4276
4285
4295
4305
4315
4325 4335
4345
4355
1
2
3
4
5
6
7
8
9 64
4365 4375
4385
4395
4406
4416
4426 4436
4446
4457
1
2
3
4
5
6
7
8
9 |
1 | 531-534 | 62
4169 4178
4188
4198
4207
4217
4227 4236
4246
42S6
1
2
3
4
5
6
7
8
9 63
4266 4276
4285
4295
4305
4315
4325 4335
4345
4355
1
2
3
4
5
6
7
8
9 64
4365 4375
4385
4395
4406
4416
4426 4436
4446
4457
1
2
3
4
5
6
7
8
9 65
4467 4477
4487
4498
4508
4519
4529 4539
4550
4560
1
2
3
4
5
6
7
8
9 |
1 | 532-535 | 63
4266 4276
4285
4295
4305
4315
4325 4335
4345
4355
1
2
3
4
5
6
7
8
9 64
4365 4375
4385
4395
4406
4416
4426 4436
4446
4457
1
2
3
4
5
6
7
8
9 65
4467 4477
4487
4498
4508
4519
4529 4539
4550
4560
1
2
3
4
5
6
7
8
9 66
4571 4581
4592
4603
4613
4624
4634 4645
4656
4667
1
2
3
4
5
6
7
9
10 |
1 | 533-536 | 64
4365 4375
4385
4395
4406
4416
4426 4436
4446
4457
1
2
3
4
5
6
7
8
9 65
4467 4477
4487
4498
4508
4519
4529 4539
4550
4560
1
2
3
4
5
6
7
8
9 66
4571 4581
4592
4603
4613
4624
4634 4645
4656
4667
1
2
3
4
5
6
7
9
10 67
4677 4688
4699
4710
4721
4732
4742 4753
4764
4775
1
2
3
4
5
7
8
9
10 |
1 | 534-537 | 65
4467 4477
4487
4498
4508
4519
4529 4539
4550
4560
1
2
3
4
5
6
7
8
9 66
4571 4581
4592
4603
4613
4624
4634 4645
4656
4667
1
2
3
4
5
6
7
9
10 67
4677 4688
4699
4710
4721
4732
4742 4753
4764
4775
1
2
3
4
5
7
8
9
10 68
4786 4797
4808
4819
4831
4842
4853 4864
4875
4887
1
2
3
4
6
7
8
9
10 |
1 | 535-538 | 66
4571 4581
4592
4603
4613
4624
4634 4645
4656
4667
1
2
3
4
5
6
7
9
10 67
4677 4688
4699
4710
4721
4732
4742 4753
4764
4775
1
2
3
4
5
7
8
9
10 68
4786 4797
4808
4819
4831
4842
4853 4864
4875
4887
1
2
3
4
6
7
8
9
10 69
4898 4909
4920
4932
4943
4955
4966 4977
4989
5000
1
2
3
5
6
7
8
9
10 |
1 | 536-539 | 67
4677 4688
4699
4710
4721
4732
4742 4753
4764
4775
1
2
3
4
5
7
8
9
10 68
4786 4797
4808
4819
4831
4842
4853 4864
4875
4887
1
2
3
4
6
7
8
9
10 69
4898 4909
4920
4932
4943
4955
4966 4977
4989
5000
1
2
3
5
6
7
8
9
10 70
5012 5023
5035
5047
5058
5070
5082 5093
5105
5117
1
2
4
5
6
7
8
9
11 |
1 | 537-540 | 68
4786 4797
4808
4819
4831
4842
4853 4864
4875
4887
1
2
3
4
6
7
8
9
10 69
4898 4909
4920
4932
4943
4955
4966 4977
4989
5000
1
2
3
5
6
7
8
9
10 70
5012 5023
5035
5047
5058
5070
5082 5093
5105
5117
1
2
4
5
6
7
8
9
11 71
5129 5140
5152
5164
5176
5188
5200 5212
5224
5236
1
2
4
5
6
7
8
10 11 |
1 | 538-541 | 69
4898 4909
4920
4932
4943
4955
4966 4977
4989
5000
1
2
3
5
6
7
8
9
10 70
5012 5023
5035
5047
5058
5070
5082 5093
5105
5117
1
2
4
5
6
7
8
9
11 71
5129 5140
5152
5164
5176
5188
5200 5212
5224
5236
1
2
4
5
6
7
8
10 11 72 5248 5260
5272
5284
5297
5309
5321 5333
5346
5358
1
2
4
5
6
7
9
10 11 |
1 | 539-542 | 70
5012 5023
5035
5047
5058
5070
5082 5093
5105
5117
1
2
4
5
6
7
8
9
11 71
5129 5140
5152
5164
5176
5188
5200 5212
5224
5236
1
2
4
5
6
7
8
10 11 72 5248 5260
5272
5284
5297
5309
5321 5333
5346
5358
1
2
4
5
6
7
9
10 11 73 5370 5383
5395
5408
5420
5433
5445 5458
5470
5483
1
3
4
5
6
8
9
10 11 |
1 | 540-543 | 71
5129 5140
5152
5164
5176
5188
5200 5212
5224
5236
1
2
4
5
6
7
8
10 11 72 5248 5260
5272
5284
5297
5309
5321 5333
5346
5358
1
2
4
5
6
7
9
10 11 73 5370 5383
5395
5408
5420
5433
5445 5458
5470
5483
1
3
4
5
6
8
9
10 11 74
5495 5508
5521
5534
5546
5559
5572 5585
5598
5610
1
3
4
5
6
8
9
10 12 |
1 | 541-544 | 72 5248 5260
5272
5284
5297
5309
5321 5333
5346
5358
1
2
4
5
6
7
9
10 11 73 5370 5383
5395
5408
5420
5433
5445 5458
5470
5483
1
3
4
5
6
8
9
10 11 74
5495 5508
5521
5534
5546
5559
5572 5585
5598
5610
1
3
4
5
6
8
9
10 12 75
5623 5636
5649
5662
5675
5689
5702 5715
5728
5741
1
3
4
5
7
8
9
10 12 |
1 | 542-545 | 73 5370 5383
5395
5408
5420
5433
5445 5458
5470
5483
1
3
4
5
6
8
9
10 11 74
5495 5508
5521
5534
5546
5559
5572 5585
5598
5610
1
3
4
5
6
8
9
10 12 75
5623 5636
5649
5662
5675
5689
5702 5715
5728
5741
1
3
4
5
7
8
9
10 12 76
5754 5768
5781
5794
5808
5821
5834 5848
5861
5875
1
3
4
5
7
8
9
11 12 |
1 | 543-546 | 74
5495 5508
5521
5534
5546
5559
5572 5585
5598
5610
1
3
4
5
6
8
9
10 12 75
5623 5636
5649
5662
5675
5689
5702 5715
5728
5741
1
3
4
5
7
8
9
10 12 76
5754 5768
5781
5794
5808
5821
5834 5848
5861
5875
1
3
4
5
7
8
9
11 12 77
5888 5902
5916
5929
5943
5957
5970 5984
5998
6012
1
3
4
5
7
8
10
11 12 |
1 | 544-547 | 75
5623 5636
5649
5662
5675
5689
5702 5715
5728
5741
1
3
4
5
7
8
9
10 12 76
5754 5768
5781
5794
5808
5821
5834 5848
5861
5875
1
3
4
5
7
8
9
11 12 77
5888 5902
5916
5929
5943
5957
5970 5984
5998
6012
1
3
4
5
7
8
10
11 12 78 6026
6039
6053
6067
6081
6095
6109 6124
6138
6152
1
3
4
6
7
8
10
11 13 |
1 | 545-548 | 76
5754 5768
5781
5794
5808
5821
5834 5848
5861
5875
1
3
4
5
7
8
9
11 12 77
5888 5902
5916
5929
5943
5957
5970 5984
5998
6012
1
3
4
5
7
8
10
11 12 78 6026
6039
6053
6067
6081
6095
6109 6124
6138
6152
1
3
4
6
7
8
10
11 13 79
6166 6180
6194
6209
6223
6237
6252 6266
6281
6295
1
3
4
6
7
9
10
11 13 |
1 | 546-549 | 77
5888 5902
5916
5929
5943
5957
5970 5984
5998
6012
1
3
4
5
7
8
10
11 12 78 6026
6039
6053
6067
6081
6095
6109 6124
6138
6152
1
3
4
6
7
8
10
11 13 79
6166 6180
6194
6209
6223
6237
6252 6266
6281
6295
1
3
4
6
7
9
10
11 13 80
6310 6324
6339
6353
6368
6383
6397 6412
6427
6442
1
3
4
6
7
9
10
12 13 |
1 | 547-550 | 78 6026
6039
6053
6067
6081
6095
6109 6124
6138
6152
1
3
4
6
7
8
10
11 13 79
6166 6180
6194
6209
6223
6237
6252 6266
6281
6295
1
3
4
6
7
9
10
11 13 80
6310 6324
6339
6353
6368
6383
6397 6412
6427
6442
1
3
4
6
7
9
10
12 13 81
6457 6471
6486
6501
6516
6531
6546 6561
6577
6592
2
3
5
6
8
9
11
12 14 |
1 | 548-551 | 79
6166 6180
6194
6209
6223
6237
6252 6266
6281
6295
1
3
4
6
7
9
10
11 13 80
6310 6324
6339
6353
6368
6383
6397 6412
6427
6442
1
3
4
6
7
9
10
12 13 81
6457 6471
6486
6501
6516
6531
6546 6561
6577
6592
2
3
5
6
8
9
11
12 14 82
6607 6622
6637
6653
6668
6683
6699 6714
6730
6745
2
3
5
6
8
9
11
12 14 |
1 | 549-552 | 80
6310 6324
6339
6353
6368
6383
6397 6412
6427
6442
1
3
4
6
7
9
10
12 13 81
6457 6471
6486
6501
6516
6531
6546 6561
6577
6592
2
3
5
6
8
9
11
12 14 82
6607 6622
6637
6653
6668
6683
6699 6714
6730
6745
2
3
5
6
8
9
11
12 14 83
6761 6776
6792
6808
6823
6839
6855 6871
6887
6902
2
3
5
6
8
9
11
1314 |
1 | 550-553 | 81
6457 6471
6486
6501
6516
6531
6546 6561
6577
6592
2
3
5
6
8
9
11
12 14 82
6607 6622
6637
6653
6668
6683
6699 6714
6730
6745
2
3
5
6
8
9
11
12 14 83
6761 6776
6792
6808
6823
6839
6855 6871
6887
6902
2
3
5
6
8
9
11
1314 84
6918 6934
6950
6966
6982
6998
7015 7031
7047
7063
2
3
5
6
8
10
11
13 15 |
1 | 551-554 | 82
6607 6622
6637
6653
6668
6683
6699 6714
6730
6745
2
3
5
6
8
9
11
12 14 83
6761 6776
6792
6808
6823
6839
6855 6871
6887
6902
2
3
5
6
8
9
11
1314 84
6918 6934
6950
6966
6982
6998
7015 7031
7047
7063
2
3
5
6
8
10
11
13 15 85
7079 7096
7112
7129
7145
7161
7178 7194
7211
7228
2
3
5
7
8
10
12
13 15 |
1 | 552-555 | 83
6761 6776
6792
6808
6823
6839
6855 6871
6887
6902
2
3
5
6
8
9
11
1314 84
6918 6934
6950
6966
6982
6998
7015 7031
7047
7063
2
3
5
6
8
10
11
13 15 85
7079 7096
7112
7129
7145
7161
7178 7194
7211
7228
2
3
5
7
8
10
12
13 15 86
7244 7261
7278
7295
7311
7328
7345 7362
7379
7396
2
3
5
7
8
10
12
13 15 |
1 | 553-556 | 84
6918 6934
6950
6966
6982
6998
7015 7031
7047
7063
2
3
5
6
8
10
11
13 15 85
7079 7096
7112
7129
7145
7161
7178 7194
7211
7228
2
3
5
7
8
10
12
13 15 86
7244 7261
7278
7295
7311
7328
7345 7362
7379
7396
2
3
5
7
8
10
12
13 15 87
7413 7430
7447
7464
7482
7499
7516 7534
7551
7568
2
3
5
7
9
10
12
14 16 |
1 | 554-557 | 85
7079 7096
7112
7129
7145
7161
7178 7194
7211
7228
2
3
5
7
8
10
12
13 15 86
7244 7261
7278
7295
7311
7328
7345 7362
7379
7396
2
3
5
7
8
10
12
13 15 87
7413 7430
7447
7464
7482
7499
7516 7534
7551
7568
2
3
5
7
9
10
12
14 16 88
7586 7603
7621
7638
7656
7674
7691 7709
7727
7745
2
4
5
7
9
11
12
14 16 |
1 | 555-558 | 86
7244 7261
7278
7295
7311
7328
7345 7362
7379
7396
2
3
5
7
8
10
12
13 15 87
7413 7430
7447
7464
7482
7499
7516 7534
7551
7568
2
3
5
7
9
10
12
14 16 88
7586 7603
7621
7638
7656
7674
7691 7709
7727
7745
2
4
5
7
9
11
12
14 16 89
7762 7780
7798
7816
7834
7852
7870 7889
7907
7925
2
4
5
7
9
11
13
14 16 |
1 | 556-559 | 87
7413 7430
7447
7464
7482
7499
7516 7534
7551
7568
2
3
5
7
9
10
12
14 16 88
7586 7603
7621
7638
7656
7674
7691 7709
7727
7745
2
4
5
7
9
11
12
14 16 89
7762 7780
7798
7816
7834
7852
7870 7889
7907
7925
2
4
5
7
9
11
13
14 16 90
7943 7962
7980
7998
8017
8035
8054 8072
8091
8110
2
4
6
7 9 11
13
15 17 |
1 | 557-560 | 88
7586 7603
7621
7638
7656
7674
7691 7709
7727
7745
2
4
5
7
9
11
12
14 16 89
7762 7780
7798
7816
7834
7852
7870 7889
7907
7925
2
4
5
7
9
11
13
14 16 90
7943 7962
7980
7998
8017
8035
8054 8072
8091
8110
2
4
6
7 9 11
13
15 17 91
8128 8147
8166
8185
8204
8222
8241 8260
8279
8299
2
4
6
8
9
11
13
15 17 |
1 | 558-561 | 89
7762 7780
7798
7816
7834
7852
7870 7889
7907
7925
2
4
5
7
9
11
13
14 16 90
7943 7962
7980
7998
8017
8035
8054 8072
8091
8110
2
4
6
7 9 11
13
15 17 91
8128 8147
8166
8185
8204
8222
8241 8260
8279
8299
2
4
6
8
9
11
13
15 17 92
8318 8337
8356
8375
8395
8414
8433 8453
8472
8492
2
4
6
8
10
12
14
15 17 |
1 | 559-562 | 90
7943 7962
7980
7998
8017
8035
8054 8072
8091
8110
2
4
6
7 9 11
13
15 17 91
8128 8147
8166
8185
8204
8222
8241 8260
8279
8299
2
4
6
8
9
11
13
15 17 92
8318 8337
8356
8375
8395
8414
8433 8453
8472
8492
2
4
6
8
10
12
14
15 17 93
8511 8531
8551
8570
8590
8610
8630 8650
8670
8690
2
4
6
8
10
12
14
16 18 |
1 | 560-563 | 91
8128 8147
8166
8185
8204
8222
8241 8260
8279
8299
2
4
6
8
9
11
13
15 17 92
8318 8337
8356
8375
8395
8414
8433 8453
8472
8492
2
4
6
8
10
12
14
15 17 93
8511 8531
8551
8570
8590
8610
8630 8650
8670
8690
2
4
6
8
10
12
14
16 18 94
8710 8730
8750
8770
8790
8810
8831 8851
8872
8892
2
4
6
8
10
12
14
16 18 |
1 | 561-564 | 92
8318 8337
8356
8375
8395
8414
8433 8453
8472
8492
2
4
6
8
10
12
14
15 17 93
8511 8531
8551
8570
8590
8610
8630 8650
8670
8690
2
4
6
8
10
12
14
16 18 94
8710 8730
8750
8770
8790
8810
8831 8851
8872
8892
2
4
6
8
10
12
14
16 18 95
8913 8933
8954
8974
8995
9016
9036 9057
9078
9099
2
4
6
8
10
12
15
17 19 |
1 | 562-565 | 93
8511 8531
8551
8570
8590
8610
8630 8650
8670
8690
2
4
6
8
10
12
14
16 18 94
8710 8730
8750
8770
8790
8810
8831 8851
8872
8892
2
4
6
8
10
12
14
16 18 95
8913 8933
8954
8974
8995
9016
9036 9057
9078
9099
2
4
6
8
10
12
15
17 19 96
9120 9141
9162
9183
9204
9226
9247 9268
9290
9311
2
4
6
8
11
13
15
17 19 |
1 | 563-566 | 94
8710 8730
8750
8770
8790
8810
8831 8851
8872
8892
2
4
6
8
10
12
14
16 18 95
8913 8933
8954
8974
8995
9016
9036 9057
9078
9099
2
4
6
8
10
12
15
17 19 96
9120 9141
9162
9183
9204
9226
9247 9268
9290
9311
2
4
6
8
11
13
15
17 19 97
9333 9354
9376
9397
9419
9441
9462 9484
9506
9528
2
4
7
9
11
13
15
17 20 |
1 | 564-567 | 95
8913 8933
8954
8974
8995
9016
9036 9057
9078
9099
2
4
6
8
10
12
15
17 19 96
9120 9141
9162
9183
9204
9226
9247 9268
9290
9311
2
4
6
8
11
13
15
17 19 97
9333 9354
9376
9397
9419
9441
9462 9484
9506
9528
2
4
7
9
11
13
15
17 20 98
9550 9572
9594
9616
9638
9661
9683 9705
9727
9750
2
4
7
9
11
13
16
18 20 |
1 | 565-568 | 96
9120 9141
9162
9183
9204
9226
9247 9268
9290
9311
2
4
6
8
11
13
15
17 19 97
9333 9354
9376
9397
9419
9441
9462 9484
9506
9528
2
4
7
9
11
13
15
17 20 98
9550 9572
9594
9616
9638
9661
9683 9705
9727
9750
2
4
7
9
11
13
16
18 20 99
9772 9795
9817
9840
9863
9886
9908 9931
9954
9977
2
5
7
9
11
14
16
18 20
Rationalised 2023-24
After studying this Unit, you will be
able to
·
describe the formation of different
types of solutions;
·
express concentration of solution
in different units;
·
state and explain Henry’s law and
Raoult’s law;
·
distinguish between ideal and
non-ideal solutions;
·
explain deviations of real solutions
from Raoult’s law;
·
describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
·
explain abnormal colligative
properties exhibited by some
solutes in solutions |
1 | 566-569 | 97
9333 9354
9376
9397
9419
9441
9462 9484
9506
9528
2
4
7
9
11
13
15
17 20 98
9550 9572
9594
9616
9638
9661
9683 9705
9727
9750
2
4
7
9
11
13
16
18 20 99
9772 9795
9817
9840
9863
9886
9908 9931
9954
9977
2
5
7
9
11
14
16
18 20
Rationalised 2023-24
After studying this Unit, you will be
able to
·
describe the formation of different
types of solutions;
·
express concentration of solution
in different units;
·
state and explain Henry’s law and
Raoult’s law;
·
distinguish between ideal and
non-ideal solutions;
·
explain deviations of real solutions
from Raoult’s law;
·
describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
·
explain abnormal colligative
properties exhibited by some
solutes in solutions In normal life we rarely come across pure substances |
1 | 567-570 | 98
9550 9572
9594
9616
9638
9661
9683 9705
9727
9750
2
4
7
9
11
13
16
18 20 99
9772 9795
9817
9840
9863
9886
9908 9931
9954
9977
2
5
7
9
11
14
16
18 20
Rationalised 2023-24
After studying this Unit, you will be
able to
·
describe the formation of different
types of solutions;
·
express concentration of solution
in different units;
·
state and explain Henry’s law and
Raoult’s law;
·
distinguish between ideal and
non-ideal solutions;
·
explain deviations of real solutions
from Raoult’s law;
·
describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
·
explain abnormal colligative
properties exhibited by some
solutes in solutions In normal life we rarely come across pure substances Most of these are mixtures containing two or more pure
substances |
1 | 568-571 | 99
9772 9795
9817
9840
9863
9886
9908 9931
9954
9977
2
5
7
9
11
14
16
18 20
Rationalised 2023-24
After studying this Unit, you will be
able to
·
describe the formation of different
types of solutions;
·
express concentration of solution
in different units;
·
state and explain Henry’s law and
Raoult’s law;
·
distinguish between ideal and
non-ideal solutions;
·
explain deviations of real solutions
from Raoult’s law;
·
describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
·
explain abnormal colligative
properties exhibited by some
solutes in solutions In normal life we rarely come across pure substances Most of these are mixtures containing two or more pure
substances Their utility or importance in life depends
on their composition |
1 | 569-572 | In normal life we rarely come across pure substances Most of these are mixtures containing two or more pure
substances Their utility or importance in life depends
on their composition For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1 |
1 | 570-573 | Most of these are mixtures containing two or more pure
substances Their utility or importance in life depends
on their composition For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1 5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on |
1 | 571-574 | Their utility or importance in life depends
on their composition For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1 5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on In this Unit, we will consider mostly liquid
solutions and their formation |
1 | 572-575 | For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1 5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on In this Unit, we will consider mostly liquid
solutions and their formation This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties |
1 | 573-576 | 5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on In this Unit, we will consider mostly liquid
solutions and their formation This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution |
1 | 574-577 | In this Unit, we will consider mostly liquid
solutions and their formation This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution Solutions
Solutions
Almost all processes in body occur in some kind of liquid solutions |
1 | 575-578 | This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution Solutions
Solutions
Almost all processes in body occur in some kind of liquid solutions Objectives
1 |
1 | 576-579 | We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution Solutions
Solutions
Almost all processes in body occur in some kind of liquid solutions Objectives
1 1
1 |
1 | 577-580 | Solutions
Solutions
Almost all processes in body occur in some kind of liquid solutions Objectives
1 1
1 1
1 |
1 | 578-581 | Objectives
1 1
1 1
1 1
1 |
1 | 579-582 | 1
1 1
1 1
1 1
1 |
1 | 580-583 | 1
1 1
1 1
1 1
Types of
Types of
Types of
Types of
Types of
Solutions
Solutions
Solutions
Solutions
Solutions
1
Unit
Unit
Unit
Unit
Unit1
Solutions are homogeneous mixtures of two or more than two
components |
1 | 581-584 | 1
1 1
1 1
Types of
Types of
Types of
Types of
Types of
Solutions
Solutions
Solutions
Solutions
Solutions
1
Unit
Unit
Unit
Unit
Unit1
Solutions are homogeneous mixtures of two or more than two
components By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture |
1 | 582-585 | 1
1 1
Types of
Types of
Types of
Types of
Types of
Solutions
Solutions
Solutions
Solutions
Solutions
1
Unit
Unit
Unit
Unit
Unit1
Solutions are homogeneous mixtures of two or more than two
components By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture Generally, the
component that is present in the largest quantity is known as solvent |
1 | 583-586 | 1
Types of
Types of
Types of
Types of
Types of
Solutions
Solutions
Solutions
Solutions
Solutions
1
Unit
Unit
Unit
Unit
Unit1
Solutions are homogeneous mixtures of two or more than two
components By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture Generally, the
component that is present in the largest quantity is known as solvent Solvent determines the physical state in which solution exists |
1 | 584-587 | By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture Generally, the
component that is present in the largest quantity is known as solvent Solvent determines the physical state in which solution exists One or
more components present in the solution other than solvent are called
solutes |
1 | 585-588 | Generally, the
component that is present in the largest quantity is known as solvent Solvent determines the physical state in which solution exists One or
more components present in the solution other than solvent are called
solutes In this Unit we shall consider only binary solutions (i |
1 | 586-589 | Solvent determines the physical state in which solution exists One or
more components present in the solution other than solvent are called
solutes In this Unit we shall consider only binary solutions (i e |
1 | 587-590 | One or
more components present in the solution other than solvent are called
solutes In this Unit we shall consider only binary solutions (i e ,
Rationalised 2023-24
2
Chemistry
Type of Solution
Solute
Solvent
Common Examples
Gaseous Solutions
Gas
Gas
Mixture of oxygen and nitrogen gases
Liquid
Gas
Chloroform mixed with nitrogen gas
Solid
Gas
Camphor in nitrogen gas
Liquid Solutions
Gas
Liquid
Oxygen dissolved in water
Liquid
Liquid
Ethanol dissolved in water
Solid
Liquid
Glucose dissolved in water
Solid Solutions
Gas
Solid
Solution of hydrogen in palladium
Liquid
Solid
Amalgam of mercury with sodium
Solid
Solid
Copper dissolved in gold
Table 1 |
1 | 588-591 | In this Unit we shall consider only binary solutions (i e ,
Rationalised 2023-24
2
Chemistry
Type of Solution
Solute
Solvent
Common Examples
Gaseous Solutions
Gas
Gas
Mixture of oxygen and nitrogen gases
Liquid
Gas
Chloroform mixed with nitrogen gas
Solid
Gas
Camphor in nitrogen gas
Liquid Solutions
Gas
Liquid
Oxygen dissolved in water
Liquid
Liquid
Ethanol dissolved in water
Solid
Liquid
Glucose dissolved in water
Solid Solutions
Gas
Solid
Solution of hydrogen in palladium
Liquid
Solid
Amalgam of mercury with sodium
Solid
Solid
Copper dissolved in gold
Table 1 1: Types of Solutions
consisting of two components) |
1 | 589-592 | e ,
Rationalised 2023-24
2
Chemistry
Type of Solution
Solute
Solvent
Common Examples
Gaseous Solutions
Gas
Gas
Mixture of oxygen and nitrogen gases
Liquid
Gas
Chloroform mixed with nitrogen gas
Solid
Gas
Camphor in nitrogen gas
Liquid Solutions
Gas
Liquid
Oxygen dissolved in water
Liquid
Liquid
Ethanol dissolved in water
Solid
Liquid
Glucose dissolved in water
Solid Solutions
Gas
Solid
Solution of hydrogen in palladium
Liquid
Solid
Amalgam of mercury with sodium
Solid
Solid
Copper dissolved in gold
Table 1 1: Types of Solutions
consisting of two components) Here each component may be
solid, liquid or in gaseous state and are summarised in Table 1 |
1 | 590-593 | ,
Rationalised 2023-24
2
Chemistry
Type of Solution
Solute
Solvent
Common Examples
Gaseous Solutions
Gas
Gas
Mixture of oxygen and nitrogen gases
Liquid
Gas
Chloroform mixed with nitrogen gas
Solid
Gas
Camphor in nitrogen gas
Liquid Solutions
Gas
Liquid
Oxygen dissolved in water
Liquid
Liquid
Ethanol dissolved in water
Solid
Liquid
Glucose dissolved in water
Solid Solutions
Gas
Solid
Solution of hydrogen in palladium
Liquid
Solid
Amalgam of mercury with sodium
Solid
Solid
Copper dissolved in gold
Table 1 1: Types of Solutions
consisting of two components) Here each component may be
solid, liquid or in gaseous state and are summarised in Table 1 1 |
1 | 591-594 | 1: Types of Solutions
consisting of two components) Here each component may be
solid, liquid or in gaseous state and are summarised in Table 1 1 Composition of a solution can be described by expressing its
concentration |
1 | 592-595 | Here each component may be
solid, liquid or in gaseous state and are summarised in Table 1 1 Composition of a solution can be described by expressing its
concentration The latter can be expressed either qualitatively
or quantitatively |
1 | 593-596 | 1 Composition of a solution can be described by expressing its
concentration The latter can be expressed either qualitatively
or quantitatively For example, qualitatively we can say that the
solution is dilute (i |
1 | 594-597 | Composition of a solution can be described by expressing its
concentration The latter can be expressed either qualitatively
or quantitatively For example, qualitatively we can say that the
solution is dilute (i e |
1 | 595-598 | The latter can be expressed either qualitatively
or quantitatively For example, qualitatively we can say that the
solution is dilute (i e , relatively very small quantity of solute)
or it is concentrated (i |
1 | 596-599 | For example, qualitatively we can say that the
solution is dilute (i e , relatively very small quantity of solute)
or it is concentrated (i e |
1 | 597-600 | e , relatively very small quantity of solute)
or it is concentrated (i e , relatively very large quantity of
solute) |
1 | 598-601 | , relatively very small quantity of solute)
or it is concentrated (i e , relatively very large quantity of
solute) But in real life these kinds of description can add to
lot of confusion and thus the need for a quantitative description
of the solution |
1 | 599-602 | e , relatively very large quantity of
solute) But in real life these kinds of description can add to
lot of confusion and thus the need for a quantitative description
of the solution There are several ways by which we can describe the concentration
of the solution quantitatively |
1 | 600-603 | , relatively very large quantity of
solute) But in real life these kinds of description can add to
lot of confusion and thus the need for a quantitative description
of the solution There are several ways by which we can describe the concentration
of the solution quantitatively (i) Mass percentage (w/w): The mass percentage of a component of a
solution is defined as:
Mass % of a component
=
Mass of the component in the solution
100
Total mass of the solution
(1 |
1 | 601-604 | But in real life these kinds of description can add to
lot of confusion and thus the need for a quantitative description
of the solution There are several ways by which we can describe the concentration
of the solution quantitatively (i) Mass percentage (w/w): The mass percentage of a component of a
solution is defined as:
Mass % of a component
=
Mass of the component in the solution
100
Total mass of the solution
(1 1)
For example, if a solution is described by 10% glucose in water by
mass, it means that 10 g of glucose is dissolved in 90 g of water
resulting in a 100 g solution |
1 | 602-605 | There are several ways by which we can describe the concentration
of the solution quantitatively (i) Mass percentage (w/w): The mass percentage of a component of a
solution is defined as:
Mass % of a component
=
Mass of the component in the solution
100
Total mass of the solution
(1 1)
For example, if a solution is described by 10% glucose in water by
mass, it means that 10 g of glucose is dissolved in 90 g of water
resulting in a 100 g solution Concentration described by mass
percentage is commonly used in industrial chemical applications |
1 | 603-606 | (i) Mass percentage (w/w): The mass percentage of a component of a
solution is defined as:
Mass % of a component
=
Mass of the component in the solution
100
Total mass of the solution
(1 1)
For example, if a solution is described by 10% glucose in water by
mass, it means that 10 g of glucose is dissolved in 90 g of water
resulting in a 100 g solution Concentration described by mass
percentage is commonly used in industrial chemical applications For example, commercial bleaching solution contains 3 |
1 | 604-607 | 1)
For example, if a solution is described by 10% glucose in water by
mass, it means that 10 g of glucose is dissolved in 90 g of water
resulting in a 100 g solution Concentration described by mass
percentage is commonly used in industrial chemical applications For example, commercial bleaching solution contains 3 62 mass
percentage of sodium hypochlorite in water |
Subsets and Splits