Question

For a first order reaction, half life is \(5\) hour. What time is required to reduce \(10\) g of reactant to \(2.5\) g ?

• A. \(3\) hour
• B. \(4\) hour
• C. \(5\) hour
• D. \(10\) hour

Hint:

Going from 10 g to 2.5 g takes two half lives.

Answer 1

The Correct Option is D

Step 1: Understand the concept
In a first order reaction the amount of reactant halves in every half life, regardless of the starting amount.

Step 2: Count the half lives
\(10\text{ g} \xrightarrow{t_{1/2}} 5\text{ g} \xrightarrow{t_{1/2}} 2.5\text{ g}\). So two half lives are needed.

Step 3: Find the time
\[ t = 2 \times t_{1/2} = 2 \times 5 = 10\ \text{h} \]

Step 4: Check the options
3 h and 4 h are shorter than one half life of 5 h, so less than half would have decayed. 5 h gives only 5 g. Only 10 h gives 2.5 g.

Final Answer:
Two half lives take 10 hours. This is option (D). \[ \boxed{\text{(D) }10\ \text{h}} \]