Question

If $K_2Cr_2O_7$ ($200 \text{ cm}^3$, $x \times 10^{-3} \text{ M}$) reacts with $0.6 \text{ M}$, $750 \text{ cm}^3$ Mohr's salt then find value of x?

• A. 375
• B. 750
• C. 150
• D. 500

Hint:

In redox titrations, the fundamental equation is $N_1 V_1 = N_2 V_2$, where Normality $N = M \times n$-factor. For $K_2Cr_2O_7$ in acid, the $n$-factor is 6.

Answer 1

The Correct Option is A

To find the value of \( x \) in this chemical reaction, we first need to understand the stoichiometry of the reaction between potassium dichromate (\( K_2Cr_2O_7 \)) and Mohr's salt (\( FeSO_4 \cdot (NH_4)_2SO_4 \cdot 6H_2O \)). The reaction can be simplified considering their equivalent reactions in acidic medium:

The balanced chemical reaction is: 

\(K_2Cr_2O_7 + 6FeSO_4 + 6H_2SO_4 \rightarrow K_2SO_4 + Cr_2(SO_4)_3 + 3Fe_2(SO_4)_3 + 7H_2O\)

The equivalent factor for \( K_2Cr_2O_7 \) is 6 (as the change in oxidation state for the dichromate ion is +6) and for Fe²⁺ (Mohr's salt), it is 1.

The reaction shows that 1 mole of \( K_2Cr_2O_7 \) reacts with 6 moles of Fe²⁺.

1. Let the molarity of \( K_2Cr_2O_7 \) be \( x \times 10^{-3} \, \text{M} \), and its volume is \( 200 \, \text{cm}^3 = 0.2 \, \text{L} \).
2. Total moles of \( K_2Cr_2O_7 \) = \(x \times 10^{-3} \times 0.2\).
3. Molarity of Mohr's salt (FeSO₄) = \( 0.6 \, \text{M} \) and its volume is \( 750 \, \text{cm}^3 = 0.75 \, \text{L} \).
4. Total moles of Mohr's salt = \(0.6 \times 0.75 = 0.45\).
5. According to the stoichiometry of the balanced reaction:
   • 1 mole of \( K_2Cr_2O_7 \) reacts with 6 moles of Mohr's salt.
   • Thus, \(x \times 10^{-3} \times 0.2\) moles of \( K_2Cr_2O_7 \) will react with \(6 \times (x \times 10^{-3} \times 0.2)\) moles of Mohr's salt.
   • Equating the moles of Mohr's salt from both sides:
   • \(6 \times (x \times 10^{-3} \times 0.2) = 0.45\)
6. Solving for \( x \):
7. \(6 \times x \times 0.2 \times 10^{-3} = 0.45\)
8. \(1.2x \times 10^{-3} = 0.45\)
9. \(x = \frac{0.45}{1.2 \times 10^{-3}} = 375\)

Thus, the value of \( x \) is 375. Therefore, the correct answer is 375.