1.	2.0 L of ethane and 9.0 L of oxygen gasses both initially at STP were pumped into a 2.0 L reactor at 25 °C. The gas mixture was then ignited with a spark. The reactor and the reaction products were then cooled back to 25 °C.

a.	Calculate the total pressure, in kPa, of the gasses in the reactor prior to ignition


To calculate the total pressure of the gases in the reactor prior to ignition, we need to use the ideal gas law equation:

\[ PV = nRT \]

Where:
- \( P \) is the pressure
- \( V \) is the volume
- \( n \) is the number of moles of gas
- \( R \) is the ideal gas constant (\(8.314 \, \text{J/(mol·K)}\) or \(0.0821 \, \text{L·atm/(mol·K)}\))
- \( T \) is the temperature in Kelvin

First, we need to determine the number of moles of each gas. At STP (Standard Temperature and Pressure, 0°C and 1 atm), 1 mole of an ideal gas occupies 22.4 L.

### Number of moles of ethane (C₂H₆):
\[ n_{\text{C₂H₆}} = \frac{2.0 \, \text{L}}{22.4 \, \text{L/mol}} = 0.0893 \, \text{mol} \]

### Number of moles of oxygen (O₂):
\[ n_{\text{O₂}} = \frac{9.0 \, \text{L}}{22.4 \, \text{L/mol}} = 0.4018 \, \text{mol} \]

### Total number of moles of gas before ignition:
\[ n_{\text{total}} = n_{\text{C₂H₆}} + n_{\text{O₂}} = 0.0893 \, \text{mol} + 0.4018 \, \text{mol} = 0.4911 \, \text{mol} \]

### Converting temperature to Kelvin:
\[ T = 25°C + 273.15 = 298.15 \, \text{K} \]

### Volume of the reactor:
\[ V = 2.0 \, \text{L} \]

### Using the ideal gas law to find the pressure:
\[ P = \frac{nRT}{V} \]

Using \( R = 0.0821 \, \text{L·atm/(mol·K)} \):

\[ P = \frac{(0.4911 \, \text{mol})(0.0821 \, \text{L·atm/(mol·K)})(298.15 \, \text{K})}{2.0 \, \text{L}} \]

\[ P = \frac{12.0087 \, \text{L·atm}}{2.0 \, \text{L}} \]

\[ P = 6.0044 \, \text{atm} \]

### Converting atm to kPa (1 atm = 101.325 kPa):
\[ P = 6.0044 \, \text{atm} \times 101.325 \, \text{kPa/atm} = 608.45 \, \text{kPa} \]

So, the total pressure of the gases in the reactor prior to ignition is **608.45 kPa**.

Do you want details or have any questions? Here are some related questions:

1. How does the volume of gas change with temperature?
2. What is the molar volume of an ideal gas at different temperatures and pressures?
3. What happens to the gas molecules when a gas is compressed?
4. How do real gases deviate from ideal gas behavior?
5. What are the conditions of STP and how do they affect gas calculations?
6. How do you convert between different units of pressure?
7. What role does the ideal gas constant play in gas law equations?
8. How can you calculate the number of moles of gas from its mass?

**Tip:** Always ensure to convert all your units to the correct SI units when using formulas, especially in gas law equations to avoid any discrepancies.

Learn how to calculate the total pressure of ethane and oxygen gases in a reactor prior to ignition using the ideal gas law equation. Detailed step-by-step solution provided.

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