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The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.?
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The constant-volume tank contains 1 kmol of methane (CH4) underline ga...
Given:
Assumptions:
Solution:
Answer: The final pressure
- 1 kmol of methane (CH4) gas
- 3 kmol of O2 gas
- Initial temperature = 25°C = 298 K
- Initial pressure = 1 atm
- Final temperature = 1000 K
Assumptions:
- The combustion reaction is complete and the products are CO2 and H2O
- The volume of the container remains constant throughout the process
- The gases behave ideally
Solution:
- Step 1: Write the balanced chemical equation for the combustion of methane
- Step 2: Calculate the moles of O2 required for complete combustion of 1 kmol of CH4
- Step 3: Determine the limiting reactant
- Step 4: Calculate the moles of CO2 and H2O produced
- Step 5: Apply the Ideal Gas Law to calculate the final pressure
CH4 + 2O2 → CO2 + 2H2O
From the balanced chemical equation, we can see that 1 kmol of CH4 requires 2 kmol of O2 for complete combustion.
As we have 3 kmol of O2, which is more than the required 2 kmol, O2 is not the limiting reactant. Therefore, CH4 is the limiting reactant.
From the balanced chemical equation, 1 kmol of CH4 produces 1 kmol of CO2 and 2 kmol of H2O.
Using the Ideal Gas Law, we can calculate the final pressure of the gases in the container.
PV = nRT
Initial moles of gas = 1 kmol + 3 kmol = 4 kmol
Initial temperature = 298 K
Final temperature = 1000 K
Final moles of gas = 1 kmol of CO2 + 2 kmol of H2O + 3 kmol of O2 = 6 kmol
Using the Ideal Gas Law, we can calculate the final pressure:
P_final = (n_final * R * T_final) / V
where R is the universal gas constant and V is the volume of the container (which is constant).
Substituting the values, we get:
P_final = (6 * 8.314 * 1000) / V
where V is the volume of the container in m3.
As the volume of the container is constant throughout the process, we can write:
P_initial * V = n_initial * R * T_initial
P_final * V = n_final * R * T_final
Dividing the second equation by the first, we get:
P_final/P_initial = (n_final/n_initial) * (T_initial/T_final)
Substituting the values, we get:
P_final = P_initial * (n_final/n_initial) * (T_initial/T_final)
P_final = 1 atm * (6/4) * (298/1000)
P_final = 0.447 atm
Answer: The final pressure
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The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.?
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The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.?.
The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The constant-volume tank contains 1 kmol of methane (CH4) underline gas and 3 kmol of O2 at 25 degrees * C and 1 atm. The contents of the tank are ignited, and the methane gas burns completely. If the final temperature is 1000 K, determine the final pressure in the tank.?.
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