A sample of an ideal gas at 1.00 atm and a volume of 1.90 L was placed in a weighted balloon and dropped into the ocean. As the sample descended, the water pressure compressed the balloon and reduced its volume. When the pressure had increased to 80.0 atm, what was the volume of the sample? Assume that the temperature was held constant. V = L

Chemistry
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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### Problem Description:

**Ideal Gas Law Application**

A sample of an ideal gas at 1.00 atm and a volume of 1.90 L was placed in a weighted balloon and dropped into the ocean. As the sample descended, the water pressure compressed the balloon and reduced its volume. When the pressure had increased to 80.0 atm, what was the volume of the sample? Assume that the temperature was held constant.

\[ V = \underline{\hspace{50px}} \, \text{L} \]

### Explanation:

This question involves using the Ideal Gas Law, specifically Boyle's Law, which states that for a given mass of gas at constant temperature, the product of the pressure and the volume is constant. This can be expressed as:

\[ P_1 \times V_1 = P_2 \times V_2 \]

Where:
- \( P_1 = 1.00 \, \text{atm} \) is the initial pressure.
- \( V_1 = 1.90 \, \text{L} \) is the initial volume.

The task is to find \( V_2 \), the volume at the final pressure \( P_2 = 80.0 \, \text{atm} \).

Substitute the known values into the equation to solve for \( V_2 \):

\[ 1.00 \, \text{atm} \times 1.90 \, \text{L} = 80.0 \, \text{atm} \times V_2 \]

By solving this equation, one can determine the final volume \( V_2 \) of the gas.
Transcribed Image Text:### Problem Description: **Ideal Gas Law Application** A sample of an ideal gas at 1.00 atm and a volume of 1.90 L was placed in a weighted balloon and dropped into the ocean. As the sample descended, the water pressure compressed the balloon and reduced its volume. When the pressure had increased to 80.0 atm, what was the volume of the sample? Assume that the temperature was held constant. \[ V = \underline{\hspace{50px}} \, \text{L} \] ### Explanation: This question involves using the Ideal Gas Law, specifically Boyle's Law, which states that for a given mass of gas at constant temperature, the product of the pressure and the volume is constant. This can be expressed as: \[ P_1 \times V_1 = P_2 \times V_2 \] Where: - \( P_1 = 1.00 \, \text{atm} \) is the initial pressure. - \( V_1 = 1.90 \, \text{L} \) is the initial volume. The task is to find \( V_2 \), the volume at the final pressure \( P_2 = 80.0 \, \text{atm} \). Substitute the known values into the equation to solve for \( V_2 \): \[ 1.00 \, \text{atm} \times 1.90 \, \text{L} = 80.0 \, \text{atm} \times V_2 \] By solving this equation, one can determine the final volume \( V_2 \) of the gas.
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