Question

For a reaction $ 5X + Y \to 3Z $, the rate of formation of Z is $ 2.4 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} $. Calculate the average rate of disappearance of X.

• A. \( 4.8 \times 10^{-7} \, \text{mol L}^{-1} \text{s}^{-1} \)
• B. \( 13.33 \times 10^{-6} \, \text{mol L}^{-1} \text{s}^{-1} \)
• C. \( 4.0 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \)
• D. \( 12.0 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \)

Hint:

For reactions where multiple species are involved, always use the stoichiometric coefficients to relate the rates of disappearance and formation of different species.

Answer 1

The Correct Option is C

From the reaction: \[ 5X + Y \to 3Z \] We are given the rate of formation of Z as \( 2.4 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \). 
We need to find the rate of disappearance of X. The stoichiometric relationship between X and Z is given by the coefficient ratio. 
For every 3 moles of Z formed, 5 moles of X are consumed. Thus, the rate of disappearance of X can be related to the rate of formation of Z by the following equation: \[ \text{Rate of disappearance of X} = \frac{5}{3} \times \text{Rate of formation of Z} \] Substituting the given rate of formation of Z: \[ \text{Rate of disappearance of X} = \frac{5}{3} \times 2.4 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \] \[ \text{Rate of disappearance of X} = 4.0 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \] Thus, the correct answer is \( (C) \).