Consider the following decomposition reaction of ammonium carbonate ((NH4)2CO3):
(NH4)2CO3 (s) 2 NH3 (g) + CO2 (g) + H2O (g)
In one experiment at 25.0°C, a sample of pure (NH4)2CO3 is placed in an evacuated 2.00 L vessel. At
equilibrium, the total pressure is found to be 0.8944 atm.
(a) Determine the equilibrium partial pressure of each gaseous species.
(b) Determine the mass of ammonium carbonate ((NH4)2CO3) that must have reacted in order to achieve
equilibrium.
(c) Determine the value of Kp assuming that the reaction temperature is 25.0°C.
for a) I started with PV=nRT to find the moles of ammonium carbonate, but I don't know where to go from there.
All of the products are gases but I can't show that without using more than one line.
....(NH4)2CO3(s) = 2NH3 + CO2 + H2O
....solid...........2p......p.....p
So the total pressure of the system is due to the gases.
Total P = 2p + p + p = 0.8944 atm.
Solve for p and 2p and that gives you the partial pressures of each gas for part a.
b. Use PV = nRT and solve for n to find mols (NH4)2CO3 used, then convert to grams.
c. Write the Kp expression, substitute the partial pressures from a and solve for Kp.
To determine the equilibrium partial pressure of each gaseous species, you need to use the ideal gas law equation, PV = nRT. Let's go through the steps:
Step 1: Calculate the number of moles of ammonium carbonate ((NH4)2CO3) present initially in the 2.00 L vessel. Since the vessel is evacuated, there is no gas present initially, so the initial moles are equal to zero.
Step 2: Using the ideal gas law, calculate the number of moles of ammonium carbonate at equilibrium. Rearranging the equation, we have n = PV/RT. Substitute the given values:
P = 0.8944 atm
V = 2.00 L
R = 0.0821 L·atm/(mol·K)
T = 25.0°C = 298 K
n = (0.8944 atm × 2.00 L) / (0.0821 L·atm/(mol·K) × 298 K)
Step 3: Since the reaction is 1:2:1:1, the mole ratio between ammonium carbonate and the other three gases is 1:2:1:1. Therefore, if we have x moles of ammonium carbonate reacting, we would have 2x moles of NH3, x moles of CO2, and x moles of H2O.
So, the equilibrium partial pressure of NH3 (g) would be the partial pressure of NH3 times 2x:
P(NH3) = 2x × (0.8944 atm)
Similarly, the equilibrium partial pressure of CO2 (g) would be the partial pressure of CO2 times x:
P(CO2) = x × (0.8944 atm)
Finally, the equilibrium partial pressure of H2O (g) would be the partial pressure of H2O times x:
P(H2O) = x × (0.8944 atm)
For part (b), the mass of ammonium carbonate reacted to achieve equilibrium can be calculated using the mole ratio. Since the mole ratio of (NH4)2CO3:NH3 is 1:2, the moles of (NH4)2CO3 reacted is 2x. Then, you can convert the moles to grams using the molecular weight of (NH4)2CO3.
For part (c), the value of Kp can be calculated using the partial pressures of the gaseous species at equilibrium. Kp is given by:
Kp = (P(NH3))^2 × P(CO2) × P(H2O)
Substitute the values obtained in part (a) into this equation to get the value of Kp.
To find the equilibrium partial pressure of each gaseous species, you can 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, and T is the temperature.
For part (a), you already have the total pressure (P) at equilibrium, which is given as 0.8944 atm. However, you need to determine the individual partial pressures of NH3, CO2, and H2O.
Let's assume x moles of (NH4)2CO3 decomposed. Since 2 moles of NH3 are formed for every 1 mole of (NH4)2CO3 decomposed, the number of moles of NH3 produced is 2x. Similarly, the number of moles of CO2 and H2O formed would also be x.
Now, let's calculate the partial pressures:
1. Determine moles of each species:
- Moles of NH3 (n(NH3)) = 2x
- Moles of CO2 (n(CO2)) = x
- Moles of H2O (n(H2O)) = x
2. Calculate the individual partial pressures:
- Partial pressure of NH3 (P(NH3)) = (2x) * (RT / V)
- Partial pressure of CO2 (P(CO2)) = x * (RT / V)
- Partial pressure of H2O (P(H2O)) = x * (RT / V)
Now, substitute the known values:
- P(NH3) = (2x) * (R * T / V)
- P(CO2) = x * (R * T / V)
- P(H2O) = x * (R * T / V)
Since you have the total pressure given as 0.8944 atm, you can express the sum of the partial pressures:
- P(NH3) + P(CO2) + P(H2O) = 0.8944 atm
Now, substitute the expressions for partial pressures:
- (2x) * (R * T / V) + x * (R * T / V) + x * (R * T / V) = 0.8944 atm
After substituting the values, you can solve this equation to find the value of x, which represents the number of moles of (NH4)2CO3 that reacted.
This equation also gives you the answer to part (b), as the number of moles of (NH4)2CO3 reacted is x. To find the mass, you can multiply x by the molar mass of (NH4)2CO3.
For part (c), once you know the value of x, you can calculate the initial moles of (NH4)2CO3 using the known volume (2.00 L) and temperature (25.0°C). Then, you can calculate the equilibrium constant, Kp, using the expression:
- Kp = [(P(NH3))^2 * P(CO2) * P(H2O)] / [(P(NH4)2CO3)^2]
where P(NH4)2CO3 is the partial pressure of (NH4)2CO3 at equilibrium.