Question

Given below are two statements: 
Statement I: Mohr's salt is composed of only three types of ions—ferrous, ammonium, and sulphate. 
Statement II: If the molar conductance at infinite dilution of ferrous, ammonium, and sulphate ions are $ x_1 $, $ x_2 $, and $ x_3 $ $ \text{S cm}^2 \, \text{mol}^{-1} $, respectively, then the molar conductance for Mohr's salt solution at infinite dilution would be given by $ x_1 + x_2 + 2x_3 $.

• A. Both statements I and Statement II are false
• B. Statement I is false but Statement II is true
• C. Statement I is true but Statement II is false
• D. Both statements I and Statement II are true

Hint:

When calculating molar conductance at infinite dilution for ionic compounds, remember that each ion contributes to the total conductance according to its molar conductance, without any extra multiplication unless the ion is polyatomic and contributes differently.

Answer 1

The Correct Option is C

Step 1: Analyzing Statement I
Mohr's salt is composed of three ions: ferrous \( \text{Fe}^{2+} \), ammonium \( \text{NH}_4^+ \), and sulphate \( \text{SO}_4^{2-} \). 
This statement is true because Mohr's salt (also known as ammonium ferrous sulphate) contains only these three types of ions. 
Thus, Statement I is correct. 
Step 2: Analyzing Statement II
The molar conductance of a salt at infinite dilution is the sum of the molar conductances of the ions it dissociates into. For Mohr's salt, the ions involved are:
Ferrous ion \( \text{Fe}^{2+} \), with a molar conductance of \( x_1 \), Ammonium ion \( \text{NH}_4^+ \), with a molar conductance of \( x_2 \), Sulphate ion \( \text{SO}_4^{2-} \), with a molar conductance of \( x_3 \). At infinite dilution, the total molar conductance \( \lambda_{\infty} \) of Mohr's salt should be the sum of the conductances of these ions. However, Statement II suggests the wrong coefficient for the sulphate ion. The sulphate ion \( \text{SO}_4^{2-} \) is a monoatomic ion and should contribute \( x_3 \) to the total conductance, not \( 2x_3 \). 
Thus, the correct expression for the molar conductance should be: \[ \lambda_{\infty} = x_1 + x_2 + x_3 \] 
Therefore, Statement II is incorrect because it incorrectly doubles the contribution of the sulphate ion.

Answer 2

Step 1:
Mohr's salt is a double salt consisting of ferrous sulphate (FeSO₄), ammonium sulphate ((NH₄)₂SO₄), and water of crystallization. Therefore, statement I is correct. Mohr's salt indeed contains ferrous, ammonium, and sulphate ions. Hence, Statement I is true.

Step 2:
Now, consider Statement II, which states that the molar conductance for Mohr's salt is given by x₁ + x₂ + 2x₃. The molar conductance of a compound at infinite dilution is the sum of the molar conductances of its individual ions. However, Mohr's salt dissociates into 2 ions of ammonium and 1 ion of ferrous and sulphate each. Therefore, the molar conductance should be calculated as x₁ + x₂ + x₃, not x₁ + x₂ + 2x₃.

Step 3:
Since Statement II is incorrect, the correct answer is (C) Statement I is true but Statement II is false.

Final Answer:
\[ \boxed{\text{Statement I is true but Statement II is false.}} \]