Question

The rate constant for a first order reaction is \(4.606\times 10^{-3}\) s\({}^{-1}\). Calculate the time required to reduce \(2.0\) g of the reactant to \(0.2\) g .

• A. \(200\) s
• B. \(500\) s
• C. \(1000\) s
• D. \(100\) s

Hint:

Use the integrated first order rate equation with the ratio of initial to final amount equal to 10.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a first order reaction the time needed is given by \(t=\dfrac{2.303}{k}\log\dfrac{[A]_0}{[A]}\).

Step 2: Substitute the Values
Here \([A]_0=2.0\) g, \([A]=0.2\) g and \(k=4.606\times10^{-3}\ \text{s}^{-1}\).
So \(\dfrac{[A]_0}{[A]}=10\) and \(\log 10=1\).

Step 3: Calculation
\(t=\dfrac{2.303}{4.606\times10^{-3}}\times 1\)
\(t=\dfrac{2.303}{4.606\times10^{-3}}=0.5\times10^{3}\ \text{s}\).

Step 4: Compare the options
\(t=500\) s, which matches option (B).

Final Answer:
The time required is 500 s. \[ \boxed{\text{(B) }500\ \text{s}} \]