At constant temperature, the pressure of V mL of a dry gas was increased from 1 atm to 2 atm. The new volume will be :

Options

A. 2V
B. `V//2`
C. `V^(2)`
D. `V//4`

Explanation

To solve the problem of finding the new volume of a gas when its pressure is increased at constant temperature, we can use Boyle's Law, which states that the product of pressure and volume for a given mass of gas is constant when the temperature is held constant.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial pressure (P1) = 1 atm
- Initial volume (V1) = V mL
- Final pressure (P2) = 2 atm
- Final volume (V2) = ?

2. **Apply Boyle's Law:**
According to Boyle's Law, we have:
\[ P1 \times V1 = P2 \times V2 \]

3. **Substitute the Known Values:**
Plugging in the values we have:
\[ 1 \, \text{atm} \times V = 2 \, \text{atm} \times V2 \]

4. **Rearrange the Equation to Solve for V2:**
Rearranging the equation gives:
\[ V2 = \frac{P1 \times V1}{P2} \]
Substituting the known pressures:
\[ V2 = \frac{1 \, \text{atm} \times V}{2 \, \text{atm}} \]

5. **Calculate V2:**
Simplifying the equation:
\[ V2 = \frac{V}{2} \]

6. **Conclusion:**
The new volume (V2) when the pressure is increased from 1 atm to 2 atm is:
\[ V2 = \frac{V}{2} \]

### Final Answer:
The new volume will be \( \frac{V}{2} \) mL.

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