Question

For the first order reaction, the half life period is \(10\) minutes. What quantity of reactant remains after \(30\) minutes if the initial quantity of reactant taken is \(1\) g?

• A. \(0.25\ \text{g}\)
• B. \(0.33\ \text{g}\)
• C. \(0.125\ \text{g}\)
• D. \(0.0625\ \text{g}\)

Hint:

After each half life the amount of reactant is halved.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a first order reaction the amount remaining halves after every half life.

Step 2: Number of Half Lives
\(n=\dfrac{30}{10}=3\)

Step 3: Calculation
Amount left \(=1\ \text{g}\times\left(\dfrac{1}{2}\right)^{3}=0.125\ \text{g}\)

Step 4: Compare the options
This matches option (C).

Final Answer:
After 30 minutes 0.125 g of the reactant remains. \[ \boxed{\text{(C) }0.125\ \text{g}} \]