10. A gas occupies a volume of 2.5 L at a temperature of 300 K . If the temperature is increased to 450 K while the pressure remains constant, what will be the new volume of the gas?

To determine the new volume of the gas when the temperature changes while keeping the pressure constant, you can use **Charles's Law**. Charles's Law states that the volume of a gas is directly proportional to its temperature when the pressure remains constant. Mathematically, it's expressed as: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] **Given:** - Initial Volume, \( V_1 = 2.5 \, \text{L} \) - Initial Temperature, \( T_1 = 300 \, \text{K} \) - Final Temperature, \( T_2 = 450 \, \text{K} \) **To Find:** - Final Volume, \( V_2 \) **Steps:** 1. **Rearrange Charles's Law to solve for \( V_2 \):** \[ V_2 = V_1 \times \frac{T_2}{T_1} \] 2. **Plug in the known values:** \[ V_2 = 2.5 \, \text{L} \times \frac{450 \, \text{K}}{300 \, \text{K}} \] 3. **Calculate the ratio:** \[ \frac{450}{300} = 1.5 \] 4. **Determine \( V_2 \):** \[ V_2 = 2.5 \, \text{L} \times 1.5 = 3.75 \, \text{L} \] **Answer:** The new volume of the gas will be **3.75 liters**.