Question

What mass of barium chloride would be decomposed by $ 9.8 $ g of sulphuric acid if 12 gram of barium sulphate and $ 2.75 $ g of hydrogen chloride were produced in a reaction assuming that the law of conservation of mass is true?
(A) $ 5.6 $ g
(B) $ 7.8 $ g
(C) $ 3.1 $ g
(D) $ 4.95 $ g

Answer 1

Hint: This question can be answered from a knowledge of mole concept and stoichiometry. The above reactions are all examples of double displacement reactions in which the cations or the anions of the one reactant are replaced or displaced by the cations or anions of the other reactant. We shall write a balanced chemical equation and then use it to find the moles and thus mass of reactants and products.

Complete step by step solution:
As per the given question, the equations are as follows:
 $ \text{BaS}{{\text{O}}_{\text{4}}}\text{ + 2 HCl}\to \text{BaC}{{\text{l}}_{2}}+{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}} $
Here one mole of barium sulphate reacts with two moles of hydrogen chloride to form one mole of barium chloride and one mole of sulphuric acid.
As the reverse reaction occurs,
 $ \text{BaC}{{\text{l}}_{2}}+{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\to \text{BaS}{{\text{O}}_{\text{4}}}\text{ + 2 HCl} $ ,
In 98 grams of sulphuric acid, 96 gram is the weight of the sulphate radical while 2 grams is the weight of hydrogen
Therefore for $ 9.8 $ grams of sulphuric acid, $ 9.6 $ grams is the weight of the sulphate radical while $ 0.2 $ grams is the weight of hydrogen.
Given weight of hydrogen chloride = $ 2.75 $ g, $ 0.2 $ grams is the weight of hydrogen, so the weight of chlorine is $ 2.75-0.2=2.55 $ grams.
In barium sulphate, $ 9.6 $ gram is the weight of the sulphate radical, so the weight of barium = $ 12-9.6=2.4 $ grams.
Therefore the weight of barium chloride formed after the process = $ 2.4+2.55=4.95 $ grams.
Hence the correct answer is option D, assuming the law of conversion of mass.

Note:
The molecular weight of the above compounds are as follows:
Barium sulphate = $ 137+32+\left( 16\times 4 \right)=233 $ grams
Barium Chloride = $ 137+\left( 35.5\times 2 \right)=208 $ grams
Hydrogen Chloride = $ 35.5+1=36.5 $ grams
Hydrogen sulphate = $ 1+32+\left( 16\times 4 \right)=98 $ grams.