Question
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?
Ask by Delgado Lawson. in Ghana
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The new volume of the gas will be 3.75 liters.
Solution
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**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
When the temperature of a gas increases at constant pressure, its volume also increases according to Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin. So, using the formula V1/T1 = V2/T2, where V1 is the initial volume (2.5 L), T1 is the initial temperature (300 K), and T2 is the new temperature (450 K), we can solve for V2. Substituting the values gives us V2 = V1 * (T2/T1) = 2.5 L * (450 K / 300 K) = 3.75 L. The new volume of the gas will be 3.75 L. So if you're ever caught in a summer heatwave, just remember, gases like to stretch their legs too when things get hot!
