In the above first order reaction the concentration of reduces from initial concentration to in 120 — Chemical Kinetics Chemistry Question
Question
In the above first order reaction the concentration of reduces from initial concentration to in 120 minutes at 300 K. The rate constant for the reaction at 300 K is . The value of x is ________. [Given log5 = 0.6989]
💡 Solution & Explanation
**Step 1: Identify the first-order rate constant formula** For a first-order reaction: $$k = \frac{2.303}{t} \log\frac{[A_0]}{[A_t]}$$ **Step 2: Set up the concentration ratio** Given that concentration reduces from initial concentration to 1/5 of initial (implied by the answer structure): $$\frac{[A_0]}{[A_t]} = 5$$ **Step 3: Substitute known values** With t = 120 minutes: $$k = \frac{2.303}{120} \log 5$$ **Step 4: Apply the given logarithm value** $$k = \frac{2.303}{120} \times 0.6989$$ **Step 5: Calculate the rate constant** $$k = \frac{2.303 \times 0.6989}{120}$$ $$k = \frac{1.609}{120}$$ $$k = 0.01341 \text{ min}^{-1}$$ **Step 6: Express in scientific notation** $$k = 1.341 \times 10^{-2} \text{ min}^{-1}$$ Rounding to two decimal places: **x = 1.34** Therefore, the answer is 1.34.