One mole of N2 and 3 moles of H2 are placed in a flask at 375 degree celsius.?
Calculate the total pressure of the system at equilibrium if the mole fraction of NH3 is found to be 0.21. The Kp for the reaction is 4.21 x 10 raise to -4
......N2 + 3H ==> 2NH3
I.....1.....3.......0
C....-x...-3x......2x
E....1-x..3-3x.....2x
Ptotal = 1-x+3-3x+2x = 4-2x
Then XNH3 = (2x/4-2x)= 0.21
Solve for x, then evaluate pNH3, pN2 and pH2. Finally, Ptotal = the sum of the partial pressures.
To calculate the total pressure of the system at equilibrium, we need to use the ideal gas law and the concept of partial pressure.
The balanced equation for the reaction is:
N2(g) + 3H2(g) ⇌ 2NH3(g)
Given:
Mole fraction of NH3 (XNH3) = 0.21
Kp = 4.21 × 10^(-4)
Mole of N2 = 1
Mole of H2 = 3
First, calculate the total moles of gas present in the system:
Total moles of gas = mole of N2 + mole of H2 + mole of NH3
Since we don't know the mole of NH3 at equilibrium, we can represent it as "x":
Total moles of gas = (1 + 3 + x)
According to the balanced equation, 2 moles of NH3 are formed from 1 mole of N2 and 3 moles of H2.
Therefore, we can write an expression for the mole fraction of NH3 in terms of "x":
XNH3 = x / (1 + 3 + x)
Given that XNH3 = 0.21, we can solve for "x":
0.21 = x / (4 + x)
0.21(4 + x) = x
0.84 + 0.21x = x
0.79x = 0.84
x ≈ 1.063
Now we know that at equilibrium, the mole of NH3 is approximately 1.063.
To calculate the partial pressure of NH3 (PNH3), we can use the ideal gas law:
PV = nRT
Since we have the mole of NH3, we can calculate the PNH3 using the partial pressure equation:
PNH3 = XNH3 * total pressure
Next, calculate the total pressure (PTotal):
PTotal = PNH3 + PN2 + PH2
Given Kp = 4.21 × 10^(-4), we can relate the partial pressures of the gases using the expression:
Kp = (PNH3)^2 / (PN2 * PH2^3)
Rearranging the equation:
PNH3^2 = Kp * PN2 * PH2^3
Now, we can substitute the values into the equation:
PNH3^2 = (4.21 × 10^(-4)) * PN2 * (PH2^3)
Since we are given the mole of N2 and H2, we can calculate their partial pressures (PN2 and PH2) using the ideal gas law and mole fractions.
Finally, calculate the total pressure of the system:
PTotal = PNH3 + PN2 + PH2
By following these steps, you can calculate the total pressure of the system at equilibrium.