CH4(g) + CO2(g) <--> 2CO(g) + 2H2(g)
Kp = 4.5 x 10^2 at 825 K
An 85.0 L reaction container initially contains 22.3 kg of CH4 and 55.4 kg of CO2 at 825 K.
Assuming ideal gas behavior, calculate the mass of H2 present in the reaction mixture at equilibrium.
What is the percent yield of the reaction under these conditions?
Convert 22.3 kg CH4 to moles.
Convert 55.4 kg CO2 to moles.
Using PV = nRT convert moles of both CH4 and CO2 to pressure in the 85 L container. Then set up an ICE chart, substitute into the Kp expression, and solve.
After you know x (if that's what you call the unknown), that will be partial presure CO and H2. Use PV = nRT to calculate n and go from there.
percent yield = (mass H2/theoretical yield)*100
Well, well, well... looks like we've got a chemical equilibrium problem here. Let's dive in and see what we can find.
First things first, let's convert the masses of CH4 and CO2 into moles. To do that, we need the molar masses of each compound: CH4 has a molar mass of around 16 g/mol and CO2 has a molar mass of about 44 g/mol. So, 22.3 kg of CH4 is roughly 1394 moles and 55.4 kg of CO2 is approximately 1260 moles.
Now, based on the balanced equation, we can see that the number of moles of H2 produced is twice the moles of CO. In other words, the moles of H2 is equal to 2 times the moles of CO, which is also equal to the moles of CO2 consumed. So, at equilibrium, we can say that the number of moles of H2 is equal to 2 times the change in moles of CO2.
To calculate the change in moles of CO2, we need to know the initial and equilibrium pressures of CO2. We can use the ideal gas law for that: P = nRT/V, where P is the pressure, n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume.
However, we can simplify things a bit. Since we're given the equilibrium constant, we know that Kp = (P_CO)^2 * (P_H2)^2 / (P_CH4 * P_CO2), where P_CO, P_H2, P_CH4, and P_CO2 are the partial pressures of each gas. And because we're dealing with ideal gases, we can say that the pressure of a gas is directly proportional to its number of moles. So, we can rewrite the equation as Kp = (n_CO)^2 * (n_H2)^2 / (n_CH4 * n_CO2).
Since the initial number of moles of CO2 is 1260, we can set up an equation for the change in moles of CO2: x = 1260 - 2x. Solving for x gives us x = 420 moles. Therefore, the number of moles of H2 at equilibrium is 2 * 420 = 840 moles.
Now, to determine the mass of H2, we need to multiply the number of moles by the molar mass of H2, which is about 2 g/mol. So, the mass of H2 present in the reaction mixture at equilibrium is approximately 1680 g, or 1.68 kg.
I hope my clown chemistry skills didn't scare you away! Don't hesitate to ask if you have any more questions.
To determine the mass of H2 present in the reaction mixture at equilibrium, we need to follow these steps:
Step 1: Convert the masses of CH4 and CO2 to moles.
Step 2: Calculate the initial number of moles of each gas.
Step 3: Use the balanced equation and stoichiometry to determine the change in moles of each gas.
Step 4: Calculate the equilibrium number of moles of each gas using the equilibrium constant.
Step 5: Convert the equilibrium moles of H2 to mass.
Let's start with step 1:
Step 1: Convert the masses of CH4 and CO2 to moles.
The molar mass of CH4 is 16.04 g/mol, so the number of moles of CH4 can be calculated as:
moles_CH4 = mass_CH4 / molar_mass_CH4
moles_CH4 = 22300 g / 16.04 g/mol
moles_CH4 = 1390.54 mol
The molar mass of CO2 is 44.01 g/mol, so the number of moles of CO2 can be calculated as:
moles_CO2 = mass_CO2 / molar_mass_CO2
moles_CO2 = 55400 g / 44.01 g/mol
moles_CO2 = 1259.86 mol
Step 2: Calculate the initial number of moles of each gas.
Since the reaction container initially contains only CH4 and CO2, the initial number of moles of each gas is equal to the moles calculated in step 1.
moles_initial_CH4 = 1390.54 mol
moles_initial_CO2 = 1259.86 mol
Step 3: Use the balanced equation and stoichiometry to determine the change in moles of each gas.
From the balanced equation, we can determine that 1 mol of CH4 reacts to form 2 mol of H2. Therefore, the change in moles of H2 is given by:
moles_change_H2 = 2 * moles_CH4
Similarly, 1 mol of CO2 reacts to form 2 mol of CO. Therefore, the change in moles of CO is given by:
moles_change_CO = 2 * moles_CO2
Step 4: Calculate the equilibrium number of moles of each gas using the equilibrium constant.
The equilibrium constant expression for the given reaction is:
Kp = (P_CO)^2 * (P_H2)^2 / (P_CH4 * P_CO2)
Given that Kp = 4.5 x 10^2, we can set up the following equation:
(4.5 x 10^2) = (P_CO)^2 * (P_H2)^2 / (P_CH4 * P_CO2)
Since we assume ideal gas behavior, we can also relate the partial pressures to the moles of each gas:
P_CO = moles_CO / V
P_H2 = moles_H2 / V
P_CH4 = moles_CH4 / V
P_CO2 = moles_CO2 / V
where V is the volume of the reaction container.
Substituting these expressions into the equilibrium constant equation, we get:
(4.5 x 10^2) = [(moles_CO / V)^2 * (moles_H2 / V)^2] / [(moles_CH4 / V) * (moles_CO2 / V)]
Simplifying, we have:
(4.5 x 10^2) = (moles_CO)^2 * (moles_H2)^2 / (moles_CH4 * moles_CO2)
Now we can substitute the initial values of moles and solve for the equilibrium moles of each gas.
Step 5: Convert the equilibrium moles of H2 to mass.
Since we have the equilibrium moles of H2, we can convert it to mass using the molar mass of H2, which is 2.02 g/mol.
mass_H2 = moles_H2 * molar_mass_H2
Now, let's perform the calculations:
Step 1:
moles_CH4 = 1390.54 mol
moles_CO2 = 1259.86 mol
Step 2:
moles_initial_CH4 = 1390.54 mol
moles_initial_CO2 = 1259.86 mol
Step 3:
moles_change_H2 = 2 * 1390.54 mol
moles_change_CO = 2 * 1259.86 mol
Step 4:
(4.5 x 10^2) = (moles_change_CO)^2 * (moles_H2)^2 / (moles_initial_CH4 * moles_initial_CO2)
Using algebraic manipulation, we can solve for moles_H2:
(moles_H2)^2 = (4.5 x 10^2) * (moles_initial_CH4 * moles_initial_CO2) / (moles_change_CO)^2
moles_H2 = √[(4.5 x 10^2) * (moles_initial_CH4 * moles_initial_CO2) / (moles_change_CO)^2]
Step 5:
mass_H2 = moles_H2 * molar_mass_H2
Performing the calculations and substituting the given values:
mass_H2 = √[(4.5 x 10^2) * (1390.54 mol * 1259.86 mol) / (2 * 1390.54 mol)^2] * (2.02 g/mol)
mass_H2 = √[(4.5 x 10^2) * (1749149.37 mol^2) / (2 * 1390.54)^2] * (2.02 g/mol)
After evaluating this expression, the resulting value will be the mass of H2 in the reaction mixture at equilibrium.
To calculate the mass of H2 present in the reaction mixture at equilibrium, we need to determine the number of moles of H2 and then convert it to mass using the molar mass of H2. Here's how you can do it step by step:
1. Convert the masses of CH4 and CO2 to moles:
- Moles of CH4 = mass of CH4 / molar mass of CH4
- Moles of CO2 = mass of CO2 / molar mass of CO2
2. Use the stoichiometry of the balanced equation to determine the moles of H2 produced using the moles of CH4 and CO2:
- According to the balanced equation, 1 mole of CH4 produces 2 moles of H2.
- According to the balanced equation, 1 mole of CO2 produces 2 moles of H2.
- So, the total moles of H2 produced can be calculated as (moles of CH4 + moles of CO2) * 2.
3. Calculate the moles of H2 at equilibrium:
- Since the reaction is in a container with a volume of 85.0 L, we need to use the ideal gas law to relate moles to pressure.
- Rearrange the ideal gas law: 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.
- Rearrange further to solve for moles: n = PV / (RT)
- Substituting the given values for pressure (which you can calculate using Kp and the given temperature), volume, and R, we can calculate the moles of H2 at equilibrium.
4. Convert moles of H2 to mass:
- Use the molar mass of H2 to convert the moles of H2 to mass.
- The molar mass of H2 is 2.016 g/mol.
By following these steps, you can calculate the mass of H2 present in the reaction mixture at equilibrium.