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Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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### Mole Fraction and Partial Pressure Calculation

**Scenario:**
Some \( \text{N}_2 \) gas is mixed with some \( \text{O}_2 \) gas, and the sketch below shows a representative sample of the mixture. The total pressure of the mixture is measured and found to be 0.120 kPa.

**Diagram Explanation:**
- The image shows a mixture of gas molecules.
- Red circles represent oxygen molecules.
- Blue circles represent nitrogen molecules.

**Key:**
- **Carbon:** Black
- **Nitrogen:** Blue
- **Oxygen:** Red
- **Hydrogen:** White
- **Sulfur:** Yellow
- **Chlorine:** Green

**Objective:**
Calculate the mole fraction and partial pressure of each gas in this mixture. Round your answers to 3 significant digits. You may assume each gas behaves as an ideal gas.

**Calculation:**

1. **Count the Molecules:**
   - Count the number of each type of molecule in the diagram.

2. **Determine Mole Fraction:**
   The mole fraction \( (X) \) can be calculated using the formula:
   \[
   X_i = \frac{n_i}{n_{\text{total}}}
   \]
   where \( n_i \) is the number of molecules of gas \( i \), and \( n_{\text{total}} \) is the total number of gas molecules.

3. **Calculate Partial Pressure:**
   The partial pressure \( P_i \) can be calculated using Dalton's Law of Partial Pressures:
   \[
   P_i = X_i \times P_{\text{total}}
   \]
   where \( P_{\text{total}} \) is the total pressure of the gas mixture.

**Input Fields:**
Fill in the calculated values in the provided table:

\[
\begin{array}{|c|c|c|}
\hline
\text{gas} & \text{mole fraction} & \text{partial pressure} \\
\hline
\text{N}_2 &  &  \text{kPa} \\
\hline
\text{O}_2 &  &  \text{kPa} \\
\hline
\end{array}
\]
Transcribed Image Text:### Mole Fraction and Partial Pressure Calculation **Scenario:** Some \( \text{N}_2 \) gas is mixed with some \( \text{O}_2 \) gas, and the sketch below shows a representative sample of the mixture. The total pressure of the mixture is measured and found to be 0.120 kPa. **Diagram Explanation:** - The image shows a mixture of gas molecules. - Red circles represent oxygen molecules. - Blue circles represent nitrogen molecules. **Key:** - **Carbon:** Black - **Nitrogen:** Blue - **Oxygen:** Red - **Hydrogen:** White - **Sulfur:** Yellow - **Chlorine:** Green **Objective:** Calculate the mole fraction and partial pressure of each gas in this mixture. Round your answers to 3 significant digits. You may assume each gas behaves as an ideal gas. **Calculation:** 1. **Count the Molecules:** - Count the number of each type of molecule in the diagram. 2. **Determine Mole Fraction:** The mole fraction \( (X) \) can be calculated using the formula: \[ X_i = \frac{n_i}{n_{\text{total}}} \] where \( n_i \) is the number of molecules of gas \( i \), and \( n_{\text{total}} \) is the total number of gas molecules. 3. **Calculate Partial Pressure:** The partial pressure \( P_i \) can be calculated using Dalton's Law of Partial Pressures: \[ P_i = X_i \times P_{\text{total}} \] where \( P_{\text{total}} \) is the total pressure of the gas mixture. **Input Fields:** Fill in the calculated values in the provided table: \[ \begin{array}{|c|c|c|} \hline \text{gas} & \text{mole fraction} & \text{partial pressure} \\ \hline \text{N}_2 & & \text{kPa} \\ \hline \text{O}_2 & & \text{kPa} \\ \hline \end{array} \]
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