Law of reciprocal proportion

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## Law of reciprocal proportion or Law of Equivalent proportion –

*Richter gave this law.According to this law,*

*” The weights of the two or more substances which separately react with same weight of a third substance are also the weights of these substances which react with each other or in a simple multiple of them. “*

*Ex – Hydrogen combine with sulphur and oxygen to form compounds H _{2}S and H_{2}O respectively.*

*In H _{2}S 2 parts hydrogen 32 parts sulphur*

*In H _{2}O 2 parts hydrogen 16 parts oxygen*

*According to the law of reciprocal proportion sulphur should combine with oxygen in the ratio of 32 : 16*

*( 2 : 1) or a simple multiple of it.*

*In SO2,*

*sulphur and oxygen combine in the ratio of 32 : 32 or 1 : 1.*

*The two ratios are related to each other as 2/1 :1/1 = 2:1*

*This is a simple multiple ratio.*

*In SO*_{3},

_{3},

*sulphur and oxygen combine in the ratio of 32 : 48 or 2 : 3*

*The two ratios are related to each other as 2/1 : 2/3 = 3 : 1*

*This is a simple multiple ratio.*

### Question 1) H_{2}S contains 94.11 % sulphur, water contains 11.11 % hydrogen and SO_{2} contains 50 % oxygen . Show that the results are in agreement with law of reciprocal proportions.

### Solution )

* In SO*_{2 },

_{2 },

*mass of oxygen = 50 gm*

*mass of sulphur = 100 – 50 = 50 gm*

*In H*_{2}O,

_{2}O,

*mass of hydrogen = 11.11 gm*

*mass of oxygen = 100 – 11.11 = 88.89 gm*

*Let us fix the mass of oxygen to 1 gm.*

*In H*_{2}O ,

_{2}O ,

*88.89 gm oxygen combine with hydrogen = 11.11*

*1 gm oxygen combine with hydrogen = 11.11 /88.89 = 0.125 gm*

*In SO*_{2},

_{2},

*50 gm of oxygen combine with sulphur = 50*

*1 gm of oxygen combine with sulphur = 50 / 50 = 1.0 gm*

*The ratio of masses of Hydrogen and sulphur which combine with the fixed mass of oxygen ( 1.0 gm) is ,*

*0.125 : 1.0 or 1 : 8*

*In H*_{2}S,

_{2}S,

*mass of sulphur = 94.11 gm*

*mass of hydrogen = 100 = 94.11 = 5.89*

*The ratio of masses of Hydrogen and sulphur in H _{2}S is ,*

*5.89 : 94.11 = 1 : 16*

*Now comparing the ratio, 1/8 : 1/16= 2 : 1*

*This is a simple whole number ratio.*

*Hence given data follows law of reciprocal proportions.*