I have been going at part B of this problem for a few hours. I've completed an ice table and calculated the total number of moles based off pressure but am still unable to come up with the partial pressures. If someone could provide the steps for solving I would appreciate it.
4. Consider the following reaction used as a rocket fuel:
(CH3)2N2H2 (s) + N2O4 (l) ⇌ 2CO2 (g) + 3N2 (g) + 4H2O (g)
Kp for this reaction is so large you can assume it goes to completion. The gases produced by this reaction were
collected in a closed, 118 L vessel, and at equilibrium, the total pressure was 2.50 atm and the temperature was
400 K.
a) Write the equilibrium constant expression (Kp) for this reaction.
b) What are the partial pressures of CO2, N2, and H2O at equilibrium?
the partial pressures are the same ratio as the product moles from the reaction equation
p CO₂ = 2/9 * 2.50 atm
p N₂ = 1/3 * 2.50 atm
p H₂O = 4/9 * 2.50 atm
To find the partial pressures of CO2, N2, and H2O at equilibrium (part B), we can use the provided information about the total pressure and the ideal gas law. Here are the steps to solve this problem:
Step 1: Write the balanced chemical equation.
(CH3)2N2H2 (s) + N2O4 (l) ⇌ 2CO2 (g) + 3N2 (g) + 4H2O (g)
Step 2: Write the equilibrium constant expression (Kp) for this reaction.
In this case, since the equation is given initially as balanced and Kp is large enough to assume the reaction goes to completion, the Kp expression is as follows:
Kp = (P_CO2)^2 / (P_CH3N2H2)(P_N2O4)
Step 3: Use the ideal gas law to relate the partial pressures of the gases to the total pressure and the mole ratio coefficients from the balanced equation.
P_CO2 = (n_CO2 * RT) / V
P_N2 = (n_N2 * RT) / V
P_H2O = (n_H2O * RT) / V
In this case, V represents the volume, R is the ideal gas constant, T is the temperature in Kelvin, and n is the number of moles.
Step 4: Set up an ICE table to determine the number of moles at equilibrium.
Since Kp is given as very large, let's assume that almost all of the reactants are consumed and converted to products. Therefore, we can assume the number of moles of reactants is negligible. This means that the number of moles of products at equilibrium is equal to the number of moles produced.
CO2: 2 moles (from the balanced equation)
N2: 3 moles (from the balanced equation)
H2O: 4 moles (from the balanced equation)
The number of moles of CH3N2H2 and N2O4 is negligible.
Step 5: Calculate the partial pressures of each gas using the ideal gas law equation from step 3.
Substitute the respective values of moles, the gas constant (R), the temperature (T), and the volume (V).
P_CO2 = (2 * R * T) / V
P_N2 = (3 * R * T) / V
P_H2O = (4 * R * T) / V
Step 6: Substitute the given values into the equations from step 5 to find the partial pressures.
Given: total pressure (P_total) = 2.50 atm
Substituting P_total = P_CO2 + P_N2 + P_H2O, we get:
2.50 = (2 * R * T) / V + (3 * R * T) / V + (4 * R * T) / V
Since the volume (V) is given as 118 L and the temperature (T) is given as 400 K, substitute these values and solve for the partial pressures.
Step 7: Calculate the partial pressures of CO2, N2, and H2O using the values obtained in step 6.
P_CO2 = (2 * R * T) / V
P_N2 = (3 * R * T) / V
P_H2O = (4 * R * T) / V
Remember to convert the pressure to the unit requested (e.g., atm).
Note: The ideal gas constant (R) has different values depending on the units of pressure. Be sure to use the appropriate value for the units you are using.
I hope this step-by-step explanation helps you solve part B of the problem.