Question

40 gm of a carbonate of an alkali metal or alkaline earth metal containing some inert impurity made to react with excess HCl solution. The liberated $CO_2$ occupied 12.315 lit. at 300 K. The correct option is

• A. Mass of impurity is 1 gm and metal is Be
• B. Mass of impurity is 3 gm and metal is Li
• C. Mass of impurity is 5 gm and metal is Be
• D. Mass of impurity is 2 gm and metal is Mg

Answer 1

Answer: (B)

Mass of impurity is 3 gm and metal is Li

Answer 2

The problem involves the reaction of a metal carbonate with excess HCl, producing carbon dioxide. We are given the total mass of the sample, the volume of CO₂ liberated, and the temperature. We need to identify the metal and the mass of the inert impurity.

1. Calculate moles of CO₂: We use the Ideal Gas Law, PV = nRT. Assuming standard atmospheric pressure P = 1 atm. Given: V = 12.315 L T = 300 K R = 0.0821 L atm mol⁻¹ K⁻¹

Number of moles of CO₂ (n) = $\frac{PV}{RT}$ $n_{CO_2} = \frac{1 \text{ atm} \times 12.315 \text{ L}}{0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \times 300 \text{ K}}$ $n_{CO_2} = \frac{12.315}{24.63}$ $n_{CO_2} = 0.5 \text{ mol}$

2. Consider the reaction stoichiometry for different types of metals:

Case A: Alkali Metal Carbonate (M₂CO₃) The reaction is: $M_2CO_3(s) + 2HCl(aq) \rightarrow 2MCl(aq) + H_2O(l) + CO_2(g)$ From the stoichiometry, 1 mole of M₂CO₃ produces 1 mole of CO₂. So, moles of M₂CO₃ = moles of CO₂ = 0.5 mol.

Let the mass of the pure metal carbonate be $m_{M_2CO_3}$. $m_{M_2CO_3} = \text{Total mass of sample} - \text{Mass of impurity}$ $m_{M_2CO_3} = 40 \text{ gm} - \text{Mass of impurity}$

Molar mass of M₂CO₃ = $\frac{m_{M_2CO_3}}{\text{moles of } M_2CO_3}$ Molar mass of M₂CO₃ = $\frac{(40 - \text{Mass of impurity})}{0.5}$ Molar mass of M₂CO₃ = $2 \times (40 - \text{Mass of impurity})$ Molar mass of M₂CO₃ = $80 - 2 \times (\text{Mass of impurity})$

Also, Molar mass of M₂CO₃ = $2 \times (\text{Atomic mass of M}) + (\text{Atomic mass of C}) + 3 \times (\text{Atomic mass of O})$ Molar mass of M₂CO₃ = $2M + 12 + 3 \times 16 = 2M + 60$

Equating the two expressions for molar mass: $2M + 60 = 80 - 2 \times (\text{Mass of impurity})$ $2M = 20 - 2 \times (\text{Mass of impurity})$ $M = 10 - (\text{Mass of impurity})$

Let's check the options involving alkali metals (Li). Option (B): Mass of impurity is 3 gm and metal is Li For Li, atomic mass M = 7. Substitute into the equation: $7 = 10 - 3$ $7 = 7$. This statement is true. Thus, option (B) is a correct option.

Case B: Alkaline Earth Metal Carbonate (MCO₃) The reaction is: $MCO_3(s) + 2HCl(aq) \rightarrow MCl_2(aq) + H_2O(l) + CO_2(g)$ From the stoichiometry, 1 mole of MCO₃ produces 1 mole of CO₂. So, moles of MCO₃ = moles of CO₂ = 0.5 mol.

Let the mass of the pure metal carbonate be $m_{MCO_3}$. $m_{MCO_3} = 40 \text{ gm} - \text{Mass of impurity}$

Molar mass of MCO₃ = $\frac{m_{MCO_3}}{\text{moles of } MCO_3}$ Molar mass of MCO₃ = $\frac{(40 - \text{Mass of impurity})}{0.5}$ Molar mass of MCO₃ = $2 \times (40 - \text{Mass of impurity})$ Molar mass of MCO₃ = $80 - 2 \times (\text{Mass of impurity})$

Also, Molar mass of MCO₃ = $(\text{Atomic mass of M}) + (\text{Atomic mass of C}) + 3 \times (\text{Atomic mass of O})$ Molar mass of MCO₃ = $M + 12 + 3 \times 16 = M + 60$

Equating the two expressions for molar mass: $M + 60 = 80 - 2 \times (\text{Mass of impurity})$ $M = 20 - 2 \times (\text{Mass of impurity})$

Let's check the options involving alkaline earth metals (Be, Mg). Option (A): Mass of impurity is 1 gm and metal is Be For Be, atomic mass M = 9. Substitute into the equation: $9 = 20 - 2 \times 1$ $9 = 20 - 2$ $9 = 18$. This statement is false. So, option (A) is incorrect.

Option (C): Mass of impurity is 5 gm and metal is Be For Be, atomic mass M = 9. Substitute into the equation: $9 = 20 - 2 \times 5$ $9 = 20 - 10$ $9 = 10$. This statement is false. So, option (C) is incorrect.

Option (D): Mass of impurity is 2 gm and metal is Mg For Mg, atomic mass M = 24. Substitute into the equation: $24 = 20 - 2 \times 2$ $24 = 20 - 4$ $24 = 16$. This statement is false. So, option (D) is incorrect.

Based on the calculations, only option (B) is consistent with the given data. Although the question is tagged as "MULTIPLE CORRECT", only one option is found to be correct. This might indicate an error in the question's tag or options.

The final answer is $\boxed{B}$