An arctic weather balloon is filled with 30.1 L of helium gas inside a prep shed. The temperature inside the shed is 8. °C. The balloon is then taken outside, where the temperature is -45. °C. Calculate the new volume of the balloon. You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits.

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Chapter1: Chemical Foundations
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**Problem:**

An arctic weather balloon is filled with 30.1 L of helium gas inside a prep shed. The temperature inside the shed is 8°C. The balloon is then taken outside, where the temperature is -45°C. Calculate the new volume of the balloon.

You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits.

**Solution:**

This problem involves the application of the Combined Gas Law, particularly focusing on Charles's Law, since pressure remains constant. Here's the solution process:

1. **Identify the given variables:**
   - Initial Volume (V₁) = 30.1 L
   - Initial Temperature (T₁) = 8°C = 8 + 273.15 = 281.15 K
   - Final Temperature (T₂) = -45°C = -45 + 273.15 = 228.15 K
   - Final Volume (V₂) = ?

2. **Use the formula for Charles's Law:**
   \[
   \frac{V₁}{T₁} = \frac{V₂}{T₂}
   \]

3. **Solve for V₂:**
   \[
   V₂ = \frac{V₁ \times T₂}{T₁} = \frac{30.1 \, \text{L} \times 228.15 \, \text{K}}{281.15 \, \text{K}}
   \]

4. **Calculate:**
   \[
   V₂ ≈ 24.4 \, \text{L}
   \]

Thus, the new volume of the balloon, after being taken outside, is approximately 24.4 liters when rounded to three significant digits.

**Note:** 
Always convert temperatures to Kelvin in gas law calculations by adding 273.15 to the Celsius temperature.
Transcribed Image Text:**Problem:** An arctic weather balloon is filled with 30.1 L of helium gas inside a prep shed. The temperature inside the shed is 8°C. The balloon is then taken outside, where the temperature is -45°C. Calculate the new volume of the balloon. You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits. **Solution:** This problem involves the application of the Combined Gas Law, particularly focusing on Charles's Law, since pressure remains constant. Here's the solution process: 1. **Identify the given variables:** - Initial Volume (V₁) = 30.1 L - Initial Temperature (T₁) = 8°C = 8 + 273.15 = 281.15 K - Final Temperature (T₂) = -45°C = -45 + 273.15 = 228.15 K - Final Volume (V₂) = ? 2. **Use the formula for Charles's Law:** \[ \frac{V₁}{T₁} = \frac{V₂}{T₂} \] 3. **Solve for V₂:** \[ V₂ = \frac{V₁ \times T₂}{T₁} = \frac{30.1 \, \text{L} \times 228.15 \, \text{K}}{281.15 \, \text{K}} \] 4. **Calculate:** \[ V₂ ≈ 24.4 \, \text{L} \] Thus, the new volume of the balloon, after being taken outside, is approximately 24.4 liters when rounded to three significant digits. **Note:** Always convert temperatures to Kelvin in gas law calculations by adding 273.15 to the Celsius temperature.
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