The half life for the first order reaction `AtoB+C` is 24 hrs.
starting with 10g of A how many grams of A will remain
after 96 hours :-

Options

A. 1.25 g
B. 0.63 g
C. 1.77 g
D. 0.5 g

Explanation

To solve the problem of how many grams of A will remain after 96 hours in a first-order reaction with a half-life of 24 hours, we can follow these steps:

### Step 1: Understand the half-life concept
The half-life (T_half) of a first-order reaction is the time required for half of the reactant to be consumed. In this case, the half-life is given as 24 hours.

### Step 2: Determine the number of half-lives in 96 hours
To find out how many half-lives fit into 96 hours, we divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{96 \text{ hours}}{24 \text{ hours}} = 4 \]

### Step 3: Calculate the remaining amount of A after each half-life
Starting with 10 grams of A, we can calculate the remaining amount after each half-life:
- After 1st half-life (24 hours):
\[ A = \frac{10 \text{ grams}}{2} = 5 \text{ grams} \]
- After 2nd half-life (48 hours):
\[ A = \frac{5 \text{ grams}}{2} = 2.5 \text{ grams} \]
- After 3rd half-life (72 hours):
\[ A = \frac{2.5 \text{ grams}}{2} = 1.25 \text{ grams} \]
- After 4th half-life (96 hours):
\[ A = \frac{1.25 \text{ grams}}{2} = 0.625 \text{ grams} \]

### Step 4: Conclusion
After 96 hours, the amount of A remaining is 0.625 grams.

### Final Answer
The amount of A remaining after 96 hours is **0.625 grams**.

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