Á balloon is filled to a volume of 6.65 × 10´ mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of 1.07 × 10“ K. What is the final volume of the balloon? Volume = mL

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Chapter1: Chemical Foundations
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**Problem Statement:**

A balloon is filled to a volume of \( 6.65 \times 10^2 \) mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of \( 1.07 \times 10^2 \) K. What is the final volume of the balloon?

**Volume =** \_\_\_\_ mL

---

In this problem, the relationship between the initial and final volumes and temperatures of a gas is explored at constant pressure, which applies Charles's Law. This law can be expressed as:

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Where:
- \( V_1 \) is the initial volume.
- \( T_1 \) is the initial temperature in Kelvin.
- \( V_2 \) is the final volume.
- \( T_2 \) is the final temperature in Kelvin. 

To solve the problem:

1. Convert the initial temperature from Celsius to Kelvin:
   \[ T_1 = 15.0°C + 273.15 = 288.15 \, K \]

2. Set up the equation using Charles's Law to find \( V_2 \):
   \[ \frac{6.65 \times 10^2 \, \text{mL}}{288.15 \, K} = \frac{V_2}{1.07 \times 10^2 \, K} \]

3. Solve for \( V_2 \):
   \[ V_2 = \frac{(6.65 \times 10^2 \, \text{mL})(1.07 \times 10^2 \, K)}{288.15 \, K} \]

Calculate to find the final volume of the balloon.
Transcribed Image Text:**Problem Statement:** A balloon is filled to a volume of \( 6.65 \times 10^2 \) mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of \( 1.07 \times 10^2 \) K. What is the final volume of the balloon? **Volume =** \_\_\_\_ mL --- In this problem, the relationship between the initial and final volumes and temperatures of a gas is explored at constant pressure, which applies Charles's Law. This law can be expressed as: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Where: - \( V_1 \) is the initial volume. - \( T_1 \) is the initial temperature in Kelvin. - \( V_2 \) is the final volume. - \( T_2 \) is the final temperature in Kelvin. To solve the problem: 1. Convert the initial temperature from Celsius to Kelvin: \[ T_1 = 15.0°C + 273.15 = 288.15 \, K \] 2. Set up the equation using Charles's Law to find \( V_2 \): \[ \frac{6.65 \times 10^2 \, \text{mL}}{288.15 \, K} = \frac{V_2}{1.07 \times 10^2 \, K} \] 3. Solve for \( V_2 \): \[ V_2 = \frac{(6.65 \times 10^2 \, \text{mL})(1.07 \times 10^2 \, K)}{288.15 \, K} \] Calculate to find the final volume of the balloon.
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