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LAW OF MILTIPLE PROPORTION:


When two elements combine to form two or more than two different compounds then the different masses of one element B which combine with fixed mass of the other element bear a simple ratio to one another.
For example: Carbon forms two oxides in oxygen

The ratio of masses of oxygen in CO and CO2 for fixed mass of carbon (12)
is 16: 32 = 1: 2.
ILLUSTRATIVE EXAMPLE (9): The law of multiple proportions is illustrated by the pair of compounds:
(A) Sodium chloride and sodium bromide     
(B) Water and heavy water
(C) Sulphur dioxide and sulphur trioxide       
(D) Magnesium hydroxide and magnesium oxide
SOLUTION:  In SO2 32 gram of suphur react with 32 gram of oxygen. Similarly for SO3 fixed mass of sulphur (32 gram) react with 48 gram of oxygen. The ratio of oxygen’s mass = 32:48 = 2:3 which support law of multiple proportions. Hence (C) is correct answer.
ILLUSTRATIVE EXAMPLE (10): Carbon is found to form two oxides, which contain 42.9% and 27.3% of carbon respectively. Show that these figures illustrate the law of multiple proportions.
SOLUTION:  
Step 1: To calculate the percentage composition of carbon and oxygen in each of the two oxides

Step 2:  To calculate the weights of carbon which combine with a fixed weight i.e., one part by weight of oxygen in each of the two oxides.
In the first oxide, 57.1 parts by weight of oxygen combine with carbon = 42.9 parts.
1 part by weight of oxygen will combine with carbon = 42.9/57.1=0.751
In the second oxide 72.7 parts by weight of oxygen combine with carbon = 27.3 parts.
1 part by weight of oxygen will combine with carbon =27.3/72=0.376
Step 3:  To compare the weights of carbon which combine with the same weight of oxygen in both the oxides-The ratio of the weights of carbon that combine with the same weight of oxygen (1 part) is 0.751: 0.376 or 2:1
Since this is a simple whole number ratio, so the above data illustrate the law of multiple proportions.

TRY YOURSELF:

Exercise (1): Metal M and chlorine combine in different proportions to form two compounds A and B. The mass ratio M: Cl is 0.895: 1 in A and 1.791: 1 in B. What law of chemical combination is illustrated?
Exercise (2): By means of the following analytical results show that law of multiple proportions is true:
Exercise (3): 1 g of a metal, having no variable valency, produces 1.67 g of its oxide when heated in air. Its carbonate contains 28.57% of the metal. How much oxide will be obtained by heating 1 g of carbonate?
Exercise (4): Phosphorous and chlorine form two compounds. The first contains 22.54% by mass of phosphorous and the second 14.88% of phosphorous. Show that these data are consistent with law of multiple proportions.
TRY YOURSELF: SOLUTION:
(1) Mass of metal which combine with 1 part of chlorine are in the ratio of 1:2, which is a simple ratio. Hence, law of multiple proportions is illustrated.
(2) The masses of mercury which combine with 1 part of chlorine are in the ratio of 2:1 which is simple ratio. Hence, law of multiple proportions is illustrated.     
(3) 0.477 g
(4) Prove yourself ….

Limitation of law of multiple proportions: Non Stoichiometric compound do not follow this law for example Fe0.93O1.

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