For a chemical reaction `t_(1 // 2)` is 2.5 hours at room temperature. How much of the reactant will be left after 7.5 hours if initial weight of reactant was 160 g?

Options

A. 10g
B. 40g
C. 80 g
D. 20g

Explanation

To solve the problem, we need to determine how much of the reactant will be left after 7.5 hours, given that the half-life (t₁/₂) of the reaction is 2.5 hours and the initial amount of reactant is 160 g.

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life of a reaction is the time taken for the concentration of a reactant to reduce to half its initial value. For this reaction, the half-life (t₁/₂) is given as 2.5 hours.

2. **Determine the Number of Half-Lives**: We need to find out how many half-lives fit into the total time of 7.5 hours.
\[ \text{Number of half-lives} = \frac{\text{Total time}}{t_{1/2}} = \frac{7.5 \text{ hours}}{2.5 \text{ hours}} = 3 \]

3. **Calculate Remaining Amount**: After each half-life, the amount of reactant is halved. Starting with 160 g:
- After 1 half-life (2.5 hours):
\[ \text{Remaining} = \frac{160 \text{ g}}{2} = 80 \text{ g} \]
- After 2 half-lives (5 hours):
\[ \text{Remaining} = \frac{80 \text{ g}}{2} = 40 \text{ g} \]
- After 3 half-lives (7.5 hours):
\[ \text{Remaining} = \frac{40 \text{ g}}{2} = 20 \text{ g} \]

4. **Final Answer**: After 7.5 hours, the amount of reactant left is **20 g**.

### Summary:
The amount of reactant left after 7.5 hours is **20 g**.