Calculate the ratio of moles of CO2 produced to moles of the original gas mixture?
A mixture of methane (CH4) and ethane (C2H6) is stored in a container at 294 mmHg. The gases are burned in air to form CO2 and H2O. If the pressure of CO2 is 351 mmHg measures at the same temperature and volume as the original mixture, calculate the ratio of moles of CO2 produced to moles of the original gas mixture?
Can someone please help me solve this question. I've been trying to figure this out forever. Please show me step by step on how to solve this. I know we have to use the ideal gas law expression for both carbon dioxide and methane and ethane gas mixture. Any help is greatly appreciated!
Thanks :)
To solve this problem, we need to use the ideal gas law and convert the pressures of CO2 and the original gas mixture to moles.
Step 1: Convert the pressures from mmHg to atm:
- The pressure of the original gas mixture is given as 294 mmHg. We need to convert it to atm by dividing by 760 mmHg/atm.
P1 = 294 mmHg / 760 mmHg/atm = 0.38684 atm
- The pressure of CO2 is given as 351 mmHg. We also need to convert it to atm.
P2 = 351 mmHg / 760 mmHg/atm = 0.46184 atm
Step 2: Use the ideal gas law to find the number of moles for each gas:
The ideal gas law equation 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.
We can rearrange the equation as follows: n = PV / RT, where P and V are the pressures and volume of each gas, and we assume T and R are constant.
Step 3: Calculate the ratio of moles of CO2 produced to moles of the original gas mixture:
- We need to find the moles of CO2 using the pressure of CO2:
n_CO2 = P2 * V / RT
- We also need to find the moles of the original gas mixture using the pressure of the mixture:
n_mixture = P1 * V / RT
- Finally, we can calculate the ratio of moles of CO2 produced to moles of the original gas mixture:
ratio = n_CO2 / n_mixture
Note: Assume the volume (V), temperature (T), and gas constant (R) are the same for both the original gas mixture and CO2.
I hope this helps! Let me know if you have any further questions.
To solve this problem, we will use the ideal gas law and the concept of stoichiometry. Here are the step-by-step instructions:
Step 1: Write down the balanced chemical equation for the combustion of methane (CH4) and ethane (C2H6):
CH4 + 2O2 -> CO2 + 2H2O
C2H6 + 7/2O2 -> 2CO2 + 3H2O
Step 2: Find the moles of CH4 and C2H6 in the original gas mixture.
Use the ideal gas law equation for each gas:
PV = nRT
n = PV/RT
Let's denote the moles of CH4 as n1 and the moles of C2H6 as n2.
Step 3: Find the moles of CO2 produced.
Since the balanced equation tells us that the ratio of CH4 to CO2 is 1:1 and the ratio of C2H6 to CO2 is 2:1, the moles of CO2 produced is equal to the moles of CH4 (n1) plus twice the moles of C2H6 (2n2).
Step 4: Calculate the ratio of moles of CO2 produced to moles of the original gas mixture.
Divide the moles of CO2 produced (from Step 3) by the sum of moles of CH4 and moles of C2H6 (n1 + n2). This will give us the required ratio.
Step 5: Substitute the given pressure values into the ideal gas law equation to find the moles of CH4 (n1) and C2H6 (n2). Use the same temperature and volume for both gases, as stated in the question.
Step 6: Substitute the calculated values from Steps 2 and 4 to find the ratio of moles of CO2 produced to moles of the original gas mixture.
I hope these steps help you solve the problem! If you need further clarification or assistance, please let me know.