at 327 degrees C, the equilibrium concentrations are [CH3OH]=0.15M, [CO]=0.24M, and [H2]=1.1M for the reaction: CH3OH(g)<-->CO(g)+2H2(g) Calculate Kp at this temperature
Kp = ([CO][H2]^2)/([CH3OH])
Kp = (0.24*(1.1)^2)/(0.15)
Kp = 3.744
To calculate Kp at a given temperature, you need to use the equation:
Kp = (P(CO) * P(H2)²) / P(CH3OH)
Where P(CO), P(H2), and P(CH3OH) are the partial pressures of CO, H2, and CH3OH, respectively.
However, you have the concentrations of CH3OH, CO, and H2, so you need to convert these concentrations to partial pressures.
First, let's convert the concentrations to partial pressures using the ideal gas law equation:
PV = nRT
Where P is the partial pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since we are given concentrations in units of Molarity (M), we can assume that the volume is 1 liter (L) for convenience.
Given:
[CH3OH] = 0.15 M
[CO] = 0.24 M
[H2] = 1.1 M
Assuming ideal gas behavior, we can consider the volume of the container to be 1 liter (L).
Let's calculate the number of moles of each gas:
n(CH3OH) = [CH3OH] * V = 0.15 mol
n(CO) = [CO] * V = 0.24 mol
n(H2) = [H2] * V = 1.1 mol
Now we can calculate the partial pressures:
P(CH3OH) = n(CH3OH) * R * T / V
P(CO) = n(CO) * R * T / V
P(H2) = n(H2) * R * T / V
Let's plug in the given values and calculate the partial pressures:
P(CH3OH) = (0.15 mol) * (0.0821 L·atm/(mol·K)) * (327 K) / (1 L) = 3.865 atm
P(CO) = (0.24 mol) * (0.0821 L·atm/(mol·K)) * (327 K) / (1 L) = 6.1848 atm
P(H2) = (1.1 mol) * (0.0821 L·atm/(mol·K)) * (327 K) / (1 L) = 35.9319 atm
Now, let's plug these values into the Kp equation:
Kp = (P(CO) * P(H2)²) / P(CH3OH)
= (6.1848 atm * (35.9319 atm)²) / 3.865 atm
= 2558.63
Therefore, the value of Kp at 327 degrees Celsius is approximately 2558.63.
To calculate the equilibrium constant Kp at a given temperature, we need to use the ideal gas law and the expression for Kp. The expression for Kp is derived from the equilibrium constant expression (Kc) by taking into account the partial pressures of the gases involved.
Step 1: Write the balanced equation for the reaction:
CH3OH(g) <---> CO(g) + 2H2(g)
Step 2: Determine the initial and equilibrium partial pressures of the gases:
The given equilibrium concentrations are [CH3OH] = 0.15 M, [CO] = 0.24 M, and [H2] = 1.1 M.
Step 3: Convert the equilibrium concentrations to partial pressures using the ideal gas law:
PV = nRT
For CH3OH:
P(CH3OH) = [CH3OH] * RT
P(CH3OH) = 0.15 M * R * T
For CO:
P(CO) = [CO] * RT
P(CO) = 0.24 M * R * T
For H2:
P(H2) = [H2] * RT
P(H2) = 1.1 M * R * T
Step 4: Substitute the partial pressures into the expression for Kp:
Kp = (P(CO) * (P(H2))^2) / P(CH3OH)
Kp = (0.24 M * R * T * (1.1 M * R * T)^2) / (0.15 M * R * T)
Step 5: Simplify the equation and cancel out the gas constant R (since it will be the same on both sides):
Kp = (0.24 * 1.1^2) / 0.15
The final expression for Kp at 327 degrees C is:
Kp = 27.67
Therefore, the equilibrium constant Kp at this temperature is 27.67.