When solid NH4HS is placed in a closed flask at 28 C, the solid dissociates according to the equation:
NH4HS(s) <=> NH3(g) + H2S(g)
The total pressure of the equilibrium mixture is 0.766 atm. Determine Kp at this temperature.
Choose one answer.
a. 0.147
b. 0.766
c. 0.587
d. 0.383
e. 1.53
NH4HS(s) <=> NH3(g) + H2S(g)
p = partial pressure.
Kp = pNH3 x pH2S
Since the total pressure is 0.766 atm, and the number of moles NH3 = number of moles H2S, won't the partial pressure of each gas be just 1/2 of the total pressure? Substitute into Kp and solve. Check my thinking.
To determine the value of Kp at this temperature, we can use the ideal gas law and write out the expression for Kp.
The ideal gas law can be expressed as:
PV = nRT
Where:
P is the pressure (in atm),
V is the volume (in L),
n is the number of moles,
R is the ideal gas constant (0.0821 L·atm·mol^−1·K^−1),
and T is the temperature (in K).
We are given the following equation for the dissociation of NH4HS:
NH4HS(s) <=> NH3(g) + H2S(g)
Let's assume that x moles of NH4HS dissociate to give x moles of NH3 and x moles of H2S.
Therefore, the initial moles would be 0 moles of NH3 and H2S, and x moles of NH4HS.
As the reaction proceeds, the moles of NH4HS decrease by x, and the moles of NH3 and H2S increase by x.
At equilibrium, the moles of NH4HS would be (x-x), which is 0 moles, and the moles of NH3 and H2S would be x moles each.
From the ideal gas law, we know that:
P(NH3) = (moles of NH3 / total moles) * total pressure
P(H2S) = (moles of H2S / total moles) * total pressure
Since the total pressure of the equilibrium mixture is given as 0.766 atm, we can substitute the moles of NH3 and H2S in the expressions for P(NH3) and P(H2S):
P(NH3) = (x / (x+x)) * 0.766 = x / (2x) * 0.766 = 0.383
P(H2S) = (x / (x+x)) * 0.766 = x / (2x) * 0.766 = 0.383
Now, we can write the expression for Kp as:
Kp = (P(NH3) * P(H2S)) / P(NH4HS)
Since P(NH4HS) would be 0 at equilibrium, we can conclude that Kp = 0.383 * 0.383 / 0 = 0.
Therefore, the answer is none of the above.
To determine Kp, we need to use the equilibrium expression, which is given by:
Kp = (P(NH3) * P(H2S)) / P(NH4HS)
We are given the total pressure of the equilibrium mixture, which is 0.766 atm. However, we need to find the partial pressures of NH3, H2S, and NH4HS.
Since NH4HS dissociates according to the equation NH4HS(s) <=> NH3(g) + H2S(g), we can assume that x moles of NH4HS dissociate and form x moles of NH3 and x moles of H2S. Therefore, the partial pressures can be expressed as:
P(NH3) = x
P(H2S) = x
P(NH4HS) = initial pressure - x
In this case, we are also given the initial pressure of NH4HS, which is equal to the total pressure of the equilibrium mixture, 0.766 atm.
Substituting the partial pressures into the equilibrium expression, we have:
Kp = (x * x) / (0.766 - x)
To determine the value of x, we can use the ideal gas law, which states:
PV = nRT
For each gas in the equation, we can write:
P(NH3) * V = n(NH3) * R * T
P(H2S) * V = n(H2S) * R * T
P(NH4HS) * V = n(NH4HS) * R * T
Since the volume, temperature, and gas constant are constant, we can derive the following:
P(NH3) / n(NH3) = P(H2S) / n(H2S) = P(NH4HS) / n(NH4HS)
Therefore, we have:
P(NH3) = P(H2S) = P(NH4HS) = x
Now, we can substitute x into the equilibrium expression:
Kp = (x * x) / (0.766 - x)
To solve for x, we need to rearrange the equation:
Kp * (0.766 - x) = x^2
Expanding and rearranging, we get:
x^2 + Kp * x - Kp * 0.766 = 0
This is a quadratic equation in terms of x. We can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = Kp, and c = -Kp * 0.766. Plug these values into the formula and solve for x.
Once you find the value of x, substitute it back into the equilibrium expression to calculate Kp:
Kp = (x * x) / (0.766 - x)
The answer will be one of the options provided.