Question

A \(\mathbf{A \to products}\) is a first order reaction. The following data is obtained for this reaction at temperature T(K). The value of \(x : y\) is
\[ \begin{array}{ccc} \text{Rate} \, (mol\, L^{-1} min^{-1}) & 0.2 & 0.4 & 1.0 \\ \text{[A]} & 0.02\, M & x\, M & y\, M \\ \end{array} \]

• A. 1 : 5
• B. 2 : 3
• C. 5 : 2
• D. 2 : 5

Hint:

For first order, rate proportional to concentration; use ratio of rates to find concentration ratio.

Answer 1

The Correct Option is D

Step 1: Write first order rate law
\[ \text{Rate} = k [A] \] Step 2: Calculate \(k\) from first data point
\[ k = \frac{0.2}{0.02} = 10 \] Step 3: Calculate \(x\) for rate 0.4
\[ 0.4 = 10 \times x \implies x = 0.04\, M \] Step 4: Calculate \(y\) for rate 1.0
\[ 1.0 = 10 \times y \implies y = 0.1\, M \] Step 5: Calculate ratio \(x : y\)
\[ \frac{0.04}{0.1} = \frac{2}{5} \] Step 6: Conclusion
Ratio \(x : y = 2 : 5\).