Consider the following reaction:
CO(g)+H2O(g)⇌CO2(g)+H2(g)
Kp=0.0611 at 2000 K
A reaction mixture initially contains a CO partial pressure of 1380 torr and a H2O partial pressure of 1730 torr at 2000 K.
Calculate the equilibrium partial pressure of CO2.
CO(g) + H₂O(g) < = > CO₂(g) + H₂(g)
P(i) 1380-torr 1730-torr 0 0
ΔP -ΔP - ΔP +ΔP +ΔP
P(eq) 1380-ΔP 1730-ΔP ΔP<Equal>ΔP
Kp = P(CO₂)∙P(H₂)/P(CO)∙P(H₂O) = (ΔP)²/(1380-ΔP)(1730-ΔP) = 0.0611
Solve for ΔP using the Quadratic Formula ...
I got ΔP = 305-torr P(CO₂)∙ ... Verified by substituting into above Kp expression => Kp = 0.061075 ~ 0.0611.
Well, let me calculate it for you! But first, let's start with the jokes. Why did the scarecrow win an award? Because he was outstanding in his field! Now, let's get down to business.
To calculate the equilibrium partial pressure of CO2, we need to use the equilibrium expression and the given values. The equilibrium expression for this reaction is:
Kp = (P_CO2 * P_H2) / (P_CO * P_H2O)
We can rearrange this equation to solve for P_CO2:
P_CO2 = (Kp * P_CO * P_H2O) / (P_H2)
Now we can substitute in the given values:
P_CO2 = (0.0611 * 1380 * 1730) / (P_H2)
Unfortunately, we don't have the value for P_H2, so we can't calculate the equilibrium partial pressure of CO2. But don't worry, I've got one more joke for you! Why don't scientists trust atoms? Because they make up everything!
To calculate the equilibrium partial pressure of CO2, we can use the equilibrium expression and the given partial pressures of CO and H2O.
The equilibrium expression for the given reaction is:
Kp = (pCO2 * pH2) / (pCO * pH2O)
Given:
Kp = 0.0611
pCO = 1380 torr
pH2O = 1730 torr
We need to solve for pCO2.
Rearranging the equilibrium expression, we get:
pCO2 = (Kp * pCO * pH2O) / pH2
Substituting the given values:
pCO2 = (0.0611 * 1380 * 1730) / pH2
Now we need to find the partial pressure of H2. To do that, we use the fact that the stoichiometric coefficient of H2 in the balanced equation is 1. This means that the partial pressure of H2 is equal to the initial partial pressure of H2O.
pH2 = pH2O = 1730 torr
Finally, substituting this value into the previous equation:
pCO2 = (0.0611 * 1380 * 1730) / 1730
Simplifying:
pCO2 = 0.0611 * 1380
pCO2 ≈ 84.258 torr
Therefore, the equilibrium partial pressure of CO2 is approximately 84.258 torr.
To calculate the equilibrium partial pressure of CO2, we can use the equilibrium expression and the given values for the initial partial pressures of CO and H2O.
The equilibrium constant expression for the reaction is given by:
Kp = (P_CO2 * P_H2) / (P_CO * P_H2O)
Where:
Kp = equilibrium constant
P_CO2 = partial pressure of CO2
P_H2 = partial pressure of H2
P_CO = partial pressure of CO
P_H2O = partial pressure of H2O
We are given the following values:
P_CO = 1380 torr
P_H2O = 1730 torr
Kp = 0.0611
Now we can rearrange the equation to solve for P_CO2:
P_CO2 = (Kp * P_CO * P_H2O) / P_H2
Let's substitute the given values into the equation:
P_CO2 = (0.0611 * 1380 torr * 1730 torr) / P_H2
To solve for P_H2, we need to use the fact that the equation is balanced, meaning the stoichiometric coefficient of CO is 1 and the stoichiometric coefficient of H2O is also 1. This means that the mole ratio of CO to H2O is 1:1.
Since the moles of CO are equal to its partial pressure, we can write:
P_CO = [CO]
Similarly, since the moles of H2O are equal to its partial pressure, we can write:
P_H2O = [H2O]
This gives us the partial pressures of CO and H2O in terms of their concentrations. We can then use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
To relate the concentrations to the partial pressures, we want to calculate the equilibrium concentrations of CO and H2O using the given partial pressures and the ideal gas law.
First, let's calculate the number of moles of CO and H2O using the ideal gas law:
n_CO = (P_CO * V) / (R * T)
n_H2O = (P_H2O * V) / (R * T)
Since the volume (V), gas constant (R), and temperature (T) are constant, we can combine them into a single constant, let's call it K, for simplicity:
n_CO = (P_CO * K)
n_H2O = (P_H2O * K)
Now we can express the concentrations of CO and H2O in terms of their partial pressures:
[CO] = n_CO / V = (P_CO * K) / V
[H2O] = n_H2O / V = (P_H2O * K) / V
Since the ratio of moles of CO to moles of H2O is 1:1, the initial concentrations of CO and H2O are equal. Therefore, we can write:
[CO] = [H2O] = (P_CO * K) / V
Substituting this expression for P_CO and P_H2O into the equation for P_CO2, we get:
P_CO2 = (0.0611 * (P_CO * K) / V * (P_H2O * K) / V) / P_H2
Simplifying,
P_CO2 = (0.0611 * P_CO * P_H2O * K^2) / (V^2 * P_H2)
Finally, you can substitute the given values of P_CO, P_H2O, K, and temperature (T) to calculate the equilibrium partial pressure of CO2.