Heliox is a helium-oxygen mixture that may be used in scuba tanks for divers working at great depths. It is also used medically as a breathing treatment. A 6.25 L tank holds helium gas at a pressure of 1804 psi. A second 6.25 L tank holds oxygen at a pressure of 479.4 psi. The two gases are mixed in a 6.25 L tank. If the temperature remains the same throughout the process, what is the pressure of the gas mixture in the tank? Assume ideal gas behavior. P = psi

Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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**Title: Calculating Gas Mixture Pressure in a Scuba Tank**

**Introduction:**

Heliox is a helium-oxygen mixture used in scuba tanks for divers operating at significant depths and is also used medically as a breathing treatment.

**Problem Statement:**

You are given:

- A 6.25 L tank containing helium gas at a pressure of 1804 psi.
- A second 6.25 L tank holding oxygen at a pressure of 479.4 psi.

The task is to determine the pressure of the gas mixture when both gases are combined into a 6.25 L tank. Assume the temperature remains constant throughout and ideal gas behavior is applicable.

**Solution:**

To find the pressure of the gas mixture, apply the principles of Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.

\[ P_{\text{total}} = P_{\text{helium}} + P_{\text{oxygen}} \]

Since both gases initially occupy separate but equal volume tanks and are then mixed in a tank of the same volume, the total pressure is calculated as follows:

\[ P_{\text{total}} = 1804 \, \text{psi} + 479.4 \, \text{psi} \]

Evaluate this to find the pressure of the gas mixture:

\[ P_{\text{total}} = 2283.4 \, \text{psi} \]

Therefore, the pressure of the gas mixture in the tank is **2283.4 psi**.

**Conclusion:**

This calculation shows how ideal gas laws can help in determining the final pressure when combining gases at constant temperature and volume, useful for applications like scuba diving and medical treatments.
Transcribed Image Text:**Title: Calculating Gas Mixture Pressure in a Scuba Tank** **Introduction:** Heliox is a helium-oxygen mixture used in scuba tanks for divers operating at significant depths and is also used medically as a breathing treatment. **Problem Statement:** You are given: - A 6.25 L tank containing helium gas at a pressure of 1804 psi. - A second 6.25 L tank holding oxygen at a pressure of 479.4 psi. The task is to determine the pressure of the gas mixture when both gases are combined into a 6.25 L tank. Assume the temperature remains constant throughout and ideal gas behavior is applicable. **Solution:** To find the pressure of the gas mixture, apply the principles of Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. \[ P_{\text{total}} = P_{\text{helium}} + P_{\text{oxygen}} \] Since both gases initially occupy separate but equal volume tanks and are then mixed in a tank of the same volume, the total pressure is calculated as follows: \[ P_{\text{total}} = 1804 \, \text{psi} + 479.4 \, \text{psi} \] Evaluate this to find the pressure of the gas mixture: \[ P_{\text{total}} = 2283.4 \, \text{psi} \] Therefore, the pressure of the gas mixture in the tank is **2283.4 psi**. **Conclusion:** This calculation shows how ideal gas laws can help in determining the final pressure when combining gases at constant temperature and volume, useful for applications like scuba diving and medical treatments.
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