One mole of N2 and three moles of H2 are placed in a flask at 375 C. Calculate the total pressure of the system at equilibrium if the mole fraction of NH3 is 0.21. The Kp for the reaction is 4.31*10^4.

I assume this to be the reaction
N2 + 3H2 --> 2NH3

Help ?

Forgot to mention: Final answer is 50 atm

To solve this problem, we can use the ideal gas law along with the concept of mole fraction and the equilibrium constant, Kp.

First, let's write the balanced chemical equation for the given reaction:
N2 + 3H2 --> 2NH3

Next, let's assign variables to the number of moles of each component:
Let x be the number of moles of NH3 formed.
Since the mole ratio between NH3 and N2 is 2:1, the number of moles of N2 consumed will be x/2.
Similarly, since the mole ratio between NH3 and H2 is 2:3, the number of moles of H2 consumed will be (3/2)*x.

The initial number of moles of each component is given as follows:
N2: 1 mole
H2: 3 moles
NH3: 0 moles (since the reaction hasn't started yet)

Now, let's consider the equilibrium conditions:
The number of moles of N2 remaining at equilibrium will be 1 - x/2.
The number of moles of H2 remaining at equilibrium will be 3 - (3/2)*x.
The number of moles of NH3 formed at equilibrium will be x.

Now, we can use the ideal gas law to relate the pressures of the gases to their respective number of moles:
PV = nRT

For each gas, we can write:
P(N2)V = (1 - x/2)RT --(1)
P(H2)V = (3 - (3/2)*x)RT --(2)
P(NH3)V = xRT --(3)

Here, V is the volume of the flask, R is the ideal gas constant, and T is the temperature in Kelvin (given as 375 C, which is 375 + 273 = 648 K).

Next, let's consider the mole fraction of NH3, given as 0.21:
The mole fraction, x(NH3), is defined as the number of moles of NH3 (x) divided by the total number of moles of all components present in the system:
x(NH3) = x / (x/2 + 3 - (3/2)*x + x)
Simplifying this equation, we get:
0.21 = x / (2x/2 + 3 - 3x/2 + x)
0.21 = x / (3 + x/2 - x/2)
0.21 = x / (3 + x/2)
0.21 = 2x / (6 + x)
0.21(6 + x) = 2x
1.26 + 0.21x = 2x
2x - 0.21x = 1.26
1.79x = 1.26
x = 1.26 / 1.79
x ≈ 0.703

Now, we can substitute this value of x back into equations (1), (2), and (3) to find the partial pressures of each gas:
From equation (1):
P(N2)V = (1 - 0.703/2)RT
P(N2) = (1 - 0.703/2)RT / V
Similarly, from equations (2) and (3), we can find P(H2) and P(NH3).

Finally, to find the total pressure of the system at equilibrium, we add up the partial pressures of all gases:
Total pressure, P(total) = P(N2) + P(H2) + P(NH3)

After calculating these individual pressures and summing them up, you should get the final answer of 50 atm.

To solve this problem, we can first set up an expression for the equilibrium constant (Kp) using the given reaction:

Kp = (P(NH3)^2) / (P(N2) * P(H2)^3)

We are given that the mole fraction of NH3 is 0.21, which means that the partial pressure of NH3 is 0.21 times the total pressure of the system at equilibrium.

Let's assume that the total pressure at equilibrium is P atm. Therefore, the partial pressure of NH3 (P(NH3)) is 0.21P atm.

We also know that the initial moles of N2 and H2 are 1 and 3 moles, respectively.

Now, let's use the ideal gas law to calculate the partial pressures of N2 (P(N2)) and H2 (P(H2)).

For N2:
PV = nRT
P(N2) = (1 mole / V) * RT, where V is the volume of the flask and R is the ideal gas constant (0.0821 L.atm/mol.K).

Similarly, for H2:
P(H2) = (3 moles / V) * RT

Now, substitute these values into the equilibrium constant expression:
Kp = (0.21P)^2 / [(1/V) * RT * (3/V) * RT^3]

Simplifying this equation, we get:
Kp = (0.0441P^2) / [9(V^4) * (R^4) * (T^4)]

We are also given that Kp = 4.31 * 10^4. Substituting this value in, we can solve for P:

4.31 * 10^4 = (0.0441P^2) / [9(V^4) * (R^4) * (T^4)]

Simplifying further, we get:
P^2 = (4.31 * 10^4 * 9(V^4) * (R^4) * (T^4)) / 0.0441

Finally, to find the total pressure at equilibrium (P), take the square root of both sides of the equation:

P = sqrt[(4.31 * 10^4 * 9(V^4) * (R^4) * (T^4)) / 0.0441]

Substitute the values for V (volume of the flask), R (ideal gas constant, 0.0821 L.atm/mol.K), and T (375 C, convert to Kelvin by adding 273.15):

P = sqrt[(4.31 * 10^4 * 9(V^4) * (0.0821^4) * (648.15^4)) / 0.0441]

Calculating the expression on the right side will give you the final answer, which is equal to 50 atm.