Question

A → P is a first order reaction. At T(K), the concentration of reactant (A) after 10 min of the reaction is \(x\) mol L\(^{-1}\). After 20 min, the concentration of A is \(y\) mol L\(^{-1}\). What is its rate constant (in min\(^{-1}\))?

• A. \(0.2303 \log \frac{x}{y}\)
• B. \(2.303 \log \frac{x}{y}\)
• C. \(2.303 \log \frac{y}{x}\)
• D. \(0.2303 \log \frac{y}{x}\)

Hint:

Rate constant for first order reaction can be calculated using concentration changes over time.

Answer 1

The Correct Option is A

For first order reaction: \[ k = \frac{1}{t_2 - t_1} \ln \frac{[A]_{t_1}}{[A]_{t_2}} = \frac{1}{10} \ln \frac{x}{y} \] Converting to log base 10: \[ k = \frac{2.303}{10} \log \frac{x}{y} = 0.2303 \log \frac{x}{y} \]