Question

If $0.5g$ of a mixture of two metals, A and B with respective equivalent weights, $12$ and $9$ displaces $560mL$ of $H$ at STP from an acid, the composition of the mixture is:
A. $40\% A,60\% B$
B. $60\% A,40\% B$
C. $30\% A,70\% B$
D. $70\% A,30\% B$

Answer 1

The number of equivalents of the metal mixture is equal to the number of equivalents of the hydrogen gas at standard conditions of temperature and pressure. The composition of a mixture is determined by the mass percentage of the individual metal in the metal mixture.

Complete answer:
According to the question,
Equivalent weight of metal A = $12$
Equivalent weight of metal B = $9$
Total mass of the given mixture = $0.5g$
Let the mass of the metal A in the given mixture be $x$.
Then the mass of the metal B in the given mixture is $(0.5 - x)$ respectively.
The number of equivalents of A = $\dfrac{x}{{12}}$
The number of equivalents of B = $\dfrac{{0.5 - x}}{9}$
The total number of equivalents of A and B together displace the equivalents of the hydrogen gas.
1 mole of hydrogen gas occupies the volume at STP = $22400mL$
1 mole of ${H_2}$ gas has = 2 equivalents of $H$ atom
Thus, 1 equivalent of $H$ atom occupies the volume at STP = $\dfrac{{22400}}{2} = 11200mL$
Number of equivalents in $11200mL$ volume of hydrogen gas = $1$
Number of equivalents in $560mL$ volume of hydrogen gas = $\dfrac{1}{{11200}} \times 560 = \dfrac{1}{{20}}$ equivalents.
According to the question, the total equivalents of A and B together displace the equivalents of the hydrogen gas. Thus, mathematically, it can be written as:
$\dfrac{x}{{12}} + \dfrac{{0.5 - x}}{9} = \dfrac{1}{{20}}$
Hence, $x = 0.2$
Thus, $A = 0.2,B = 0.5 - 0.2 = 0.3$
$\% A = \dfrac{{0.2}}{{0.5}} \times 100 = 40\%$
$\% B = \dfrac{{0.3}}{{0.5}} \times 100 = 60\%$

Hence, the correct option is A. $40\% A,60\% B$ .

Note:
Whenever the percentage composition of any mixture is determined, first the mass of individual components is calculated. Next, they are divided by the total mass of the mixture individually to calculate the percentage composition of the individual components. This is a very helpful tool in the qualitative analysis of the organic and inorganic compounds.