A mixture of CH4(g) at 0.500 atm and O2(g) at 0.750 atm is present in a 3.00-L container at 28°C. The mixture is ignited by a spark and reacts according to the equation provided below. What is the total pressure in the container, now at 44°C, after the reaction is complete? The vapor pressure of water at 44°C is 68.26 mmHg.
CH4(g) + 2O2(g) ? CO2(g) + 2H2O(l)
0.616
To find the total pressure in the container after the reaction is complete, we need to consider the following steps:
1. Calculate the initial moles of CH4 and O2:
The ideal gas law equation can be used to find the number of moles of a gas based on its pressure, volume, and temperature. The formula for the ideal gas law is: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Using the given initial conditions, we can calculate the initial moles of CH4 and O2 as follows:
- For CH4: P = 0.500 atm, V = 3.00 L, T = 28°C + 273.15 = 301.15 K
- For O2: P = 0.750 atm, V = 3.00 L, T = 28°C + 273.15 = 301.15 K
Rearranging the ideal gas law equation to solve for moles, we have:
n = PV / RT
For CH4: n_CH4 = (0.500 atm)(3.00 L) / (0.0821 L·atm/mol·K)(301.15 K)
For O2: n_O2 = (0.750 atm)(3.00 L) / (0.0821 L·atm/mol·K)(301.15 K)
2. Determine the limiting reactant:
To find the limiting reactant, we compare the number of moles of CH4 and O2 using the balanced chemical equation. According to the equation, 1 mole of CH4 reacts with 2 moles of O2.
If the moles of CH4 divided by 1 is less than the moles of O2 divided by 2, CH4 is the limiting reactant. Otherwise, O2 is the limiting reactant.
3. Calculate the number of moles of CO2 produced:
When CH4 reacts, 1 mole of CH4 produces 1 mole of CO2. Since we have calculated the moles of the limiting reactant in the previous step, we can use this information to determine the moles of CO2 produced.
4. Calculate the number of moles of H2O produced:
When CH4 reacts, 1 mole of CH4 produces 2 moles of H2O. Since we have calculated the moles of the limiting reactant in the previous step, we can use this information to determine the moles of H2O produced.
5. Calculate the final total number of moles of gas:
The final moles of gas in the container after the reaction is complete will be the sum of the moles of CO2, H2O (in liquid form), and any unreacted excess O2.
Note: Since water is in the liquid form, it does not contribute to the total pressure. Therefore, we only consider moles of CO2 and unreacted excess O2 to find the total pressure.
6. Calculate the final pressure:
To find the final pressure, we use the ideal gas law equation with the total moles of gas and the final temperature. The formula will be: P = (n_CO2 + n_O2)RT / V
- For CO2: n_CO2 is the moles of CO2 calculated in step 4.
- For O2: n_O2 is the moles of unreacted excess O2, which can be calculated by subtracting the moles of O2 reacted in step 3 from the initial moles of O2.
7. Calculate the final temperature in Kelvin:
Convert the final temperature from Celsius to Kelvin by adding 273.15.
8. Convert the final pressure from atm to mmHg:
Multiply the final pressure by 760 to convert it from atm to mmHg.
Following these steps, you should be able to calculate the total pressure in the container after the reaction is complete.