https://file.aiquickdraw.com/mathbot/file/1727604795416gwanz2ld.jpg

Let's work through the problem step by step. We are asked to calculate the mole fraction, partial pressure of each gas, and the total pressure in the tank, given the following:

- Volume of the tank, \( V = 9.00 \, \text{L} \)
- Temperature, \( T = 14.5^\circ C = 287.65 \, \text{K} \)
- Mass of carbon monoxide (CO), \( m_{\text{CO}} = 7.48 \, \text{g} \)
- Mass of sulfur hexafluoride (SF₆), \( m_{\text{SF}_6} = 14.2 \, \text{g} \)
- Both gases behave as ideal gases.

We will use the following steps:
1. **Convert mass to moles** for each gas using their molar masses.
2. **Determine the mole fractions** of each gas.
3. **Calculate the partial pressures** using the ideal gas law \( PV = nRT \).
4. **Find the total pressure** by summing the partial pressures.

### Step 1: Moles of CO and SF₆
- Molar mass of CO = 28.01 g/mol
- Molar mass of SF₆ = 146.06 g/mol

Using the formula for moles:
\[
n = \frac{m}{M}
\]

Let's calculate this first.The moles of each gas are:
- Moles of carbon monoxide (CO): \( 0.267 \, \text{mol} \)
- Moles of sulfur hexafluoride (SF₆): \( 0.0972 \, \text{mol} \)

### Step 2: Mole Fractions
The mole fraction is calculated as:
\[
\chi_{\text{gas}} = \frac{n_{\text{gas}}}{n_{\text{total}}}
\]
where \( n_{\text{total}} \) is the sum of the moles of both gases.

Let's calculate the mole fractions next.The mole fractions are:
- Mole fraction of carbon monoxide (CO): \( 0.733 \)
- Mole fraction of sulfur hexafluoride (SF₆): \( 0.267 \)

### Step 3: Calculate Partial Pressures
Using the ideal gas law \( PV = nRT \), we solve for the pressure \( P \):
\[
P = \frac{nRT}{V}
\]
where:
- \( R \) is the gas constant = \( 0.0821 \, \text{L·atm/(mol·K)} \)
- \( T = 287.65 \, \text{K} \)
- \( V = 9.00 \, \text{L} \)

Let's calculate the partial pressures of each gas.The partial pressures and total pressure in the tank are:
- Partial pressure of carbon monoxide (CO): \( 0.701 \, \text{atm} \)
- Partial pressure of sulfur hexafluoride (SF₆): \( 0.255 \, \text{atm} \)
- Total pressure in the tank: \( 0.956 \, \text{atm} \)

Would you like further details or have any questions?

Here are five related questions:
1. How would the results change if the temperature increased?
2. What would happen to the partial pressures if the volume of the tank were reduced?
3. Can you derive the ideal gas law from first principles?
4. How does non-ideal gas behavior affect the results?
5. What is the significance of the mole fraction in gas mixtures?

**Tip:** Always use significant figures in your final answers to match the precision of your given data.

A 9.00 L tank at 14.5 °C is filled with 7.48 g of carbon monoxide gas and 14.2 g of sulfur hexafluoride gas. Calculate the mole fraction and partial pressure of each gas, and the total pressure in the tank.

Calculate the mole fractions, partial pressures, and total pressure for a gas mixture of carbon monoxide and sulfur hexafluoride in a 9.00 L tank at 14.5°C. Learn how to use the ideal gas law, Dalton's law, and stoichiometry to solve this college-level chemistry problem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation