Consider the decomposition of ammonium hydrogen sulfide:
NH4Hs(s) <--> NH3(g) + H2S(g)
In a sealed flask at 25*C are 10.0 g NH4HS, ammonia with a partial pressure of .692 atm, and H2S with a partial pressure of .0532 atm. When equilibrium is established, it is found that the partial pressure of ammonia has increased by 12.4%. Calculate K for the decomp. of NH4HS at 25*C.
I'm not sure exactly how to do this, but my thoughts so far are these:
Finding K= P(NH3) * P(H2S)/1 (since NH4HS is a pure solid)
Since ammonia increased by 12.4%, I would guess that H2S would increase as well. Now, would H2S increase by the same percent as NH3(12.4 %), or by the same number of atm (.08580)?
Since 1 mol NH4HS decomposes to give 1 mol NH3 + 1 mol H2S, I think you convert the initial partial pressure of NH3 and H2S to mols, then add 12.4% to mols NH3 and recalculate partial pressure of NH3. Then subtract new mols NH3 from old mols NH3 to find the mols NH4HS that decomposed. That number of mols added to the initial mols H2S should be the mols H2S that are present at equilibrium. Then convert from mols to partial pressure. (I assumed a volume of 1 L for the PV = nRT but any volume should do as long as it doesn't change.)
Check my thinking.
(I used PV=nRT to calculate mols NH3 and added 12.4% to mols and reconverted to partial pressure NH3 OR just adding 12.4% to partial pressure of NH3 provided the same number for partial pressure NH3 at equilibrium. But for H2S, I think the key is to add the same number of mols to H2S that were added to NH3, then go backward and calculate partial pressure for H2S knowing nRT. Again, check my thinking.)
1.37 g
Your thinking is mostly correct. Here's a step-by-step guide to calculate the equilibrium constant (K) for the decomposition of ammonium hydrogen sulfide (NH4HS) at 25°C:
1. Convert the initial partial pressures of NH3 and H2S to moles:
- moles NH3 = (partial pressure NH3) * (volume) / (RT)
- moles H2S = (partial pressure H2S) * (volume) / (RT)
Here, you assume a volume of 1 L and use 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 (0.0821 atm L/mol K), and T is the temperature in Kelvin (25°C = 298 K).
2. Calculate the change in moles of NH3 due to the increase of 12.4%:
- change in moles NH3 = (12.4% of moles NH3)
This represents the increase in moles of NH3 at equilibrium.
3. Calculate the new moles of NH3 at equilibrium:
- new moles NH3 = (moles NH3) + (change in moles NH3)
4. Calculate the moles of NH4HS that decomposed:
- moles NH4HS decomposed = (moles NH3) - (new moles NH3)
5. Calculate the new moles of H2S at equilibrium:
- new moles H2S = (moles H2S) + (moles NH4HS decomposed)
Here, you assume that the decomposition of NH4HS leads to an equal increase in the moles of NH3 and H2S.
6. Convert the new moles of NH3 and H2S to partial pressures:
- partial pressure NH3 at equilibrium = (new moles NH3) * (RT) / (volume)
- partial pressure H2S at equilibrium = (new moles H2S) * (RT) / (volume)
7. Calculate the equilibrium constant K:
- K = (partial pressure NH3 at equilibrium) * (partial pressure H2S at equilibrium)
Note that NH4HS, being a pure solid, does not appear in the equilibrium expression and is not used to calculate K.
By following these steps, you can calculate the equilibrium constant (K) for the decomposition of NH4HS at 25°C using the given information.
Your thinking is on the right track. To calculate the equilibrium constant, K, for the decomposition of ammonium hydrogen sulfide (NH4HS), you can use the equation:
K = (P(NH3) * P(H2S))/1
Since NH4HS is a pure solid, its concentration is considered to be constant and therefore does not appear in the equation.
To find the equilibrium partial pressures of NH3 and H2S, you first need to determine the initial moles of NH3 and H2S in the flask.
Using the ideal gas law, PV = nRT, you can calculate the initial number of moles of NH3 and H2S:
n(NH3) = (P(NH3) * V)/(RT)
n(H2S) = (P(H2S) * V)/(RT)
Here, P(NH3) and P(H2S) are the initial partial pressures of NH3 and H2S, V is the volume of the flask (which is not mentioned in the question), R is the ideal gas constant, and T is the temperature in Kelvin (25°C = 298 K).
Next, you need to calculate the new partial pressure of NH3 at equilibrium. Since the partial pressure of NH3 has increased by 12.4%, you can calculate the new partial pressure by multiplying the initial partial pressure of NH3 by 1.124.
Now, you can determine the change in moles of NH3 that occurred using the equation:
Δn(NH3) = n(NH3)_eq - n(NH3)_initial
where n(NH3)_eq is the equilibrium number of moles of NH3 and n(NH3)_initial is the initial number of moles of NH3.
Since 1 mole of NH4HS decomposes to give 1 mole of NH3, the change in moles of NH3 is equal to the moles of NH4HS that decomposed.
The mols of NH4HS that decomposed added to the initial moles of H2S should be the moles of H2S present at equilibrium.
Then, convert the number of moles of NH3 and H2S to their respective equilibrium partial pressures using the ideal gas law.
Finally, substitute the equilibrium partial pressures of NH3 and H2S into the equilibrium constant expression to calculate K.