Answer:
a) [COHNH₂] = 0.001 mol/L, [NH₃] = [CO] = 0.085 mol/L
b) 5.59 atm
Explanation:
a) The decomposition reaction of formamide is the following:
COHNH₂(d) ⇆ NH₃(g) + CO(g)
The equilibrium constant of the reaction above is:
[tex]K_{c} = \frac{[NH_{3}][CO]}{[COHNH_{2}]} = 4.84 (400 K)[/tex]
The initial concentration of formamide is:
[tex] C_{COHNH_{2}} = \frac{\eta}{V} = \frac{0.186 moles}{2.16 L} = 0.086 mol/L [/tex]
Where: η is the number of moles and V is the volume
Now, in the equilibrium the concentration of all species is:
COHNH₂(d) ⇆ NH₃(g) + CO(g)
0.086 - x x x
[tex] K_{c} = \frac{[NH_{3}][CO]}{[COHNH_{2}]} = \frac{x*x}{0.086 - x} [/tex]
[tex] 4.84*(0.086 - x) -x^{2} = 0 [/tex]
By solving the above equation for x we have:
x = 0.085 mol/L = [NH₃] = [CO]
[COHNH₂] = 0.086 - 0.085 = 0.001 mol/L
Therefore, the concentrations of all species present at equilibrium at 400 K is [NH₃] = [CO] = 0.085 mol/L and [COHNH₂] = 0.001 mol/L.
b) To find the total pressure in the container we need to find first the constant Kp as follows:
[tex] K_{p} = K_{c}*RT^{\Delta n} [/tex]
Where R is the gas constant = 0.082 Latm/(Kmol), T is the temperature = 400 K and Δn = 1
[tex] K_{p} = K_{c}*RT^{\Delta n} = 4.84*(0.082*400)^{1} = 158.8 [/tex]
Now, the total pressure is:
[tex] p_{T} = p_{COHNH_{2}} + p_{NH_{3}} + p_{CO} [/tex]
The pressure of COHNH₂ can be found using Ideal Gas Law:
[tex] P = \frac{nRT}{V} = \frac{0.186 moles*0.082 L*atm/(K*mol)*400 K}{2.16 L} = 2.82 atm [/tex]
Using the equilibrium constant we can find the pressure of NH₃ and CO:
COHNH₂(d) ⇆ NH₃(g) + CO(g)
2.82 - x x x
[tex] K_{p} = \frac{P_{NH_{3}}*P_{CO}}{P_{COHNH_{2}}} [/tex]
[tex] 158.8*(2.82 - x) - x^{2} = 0 [/tex]
By solving the above equation for x we have:
[tex] x = P_{NH_{3}} = P_{CO} = 2.77 atm [/tex]
[tex] P_{COHNH_{2}} = 2.82 - 2.77 = 0.05 atm [/tex]
Thus, the total pressure is:
[tex] p_{T} = p_{COHNH_{2}} + p_{NH_{3}} + p_{CO} = (0.05 + 2.77 + 2.77) atm = 5.59 atm [/tex]
Hence, the total pressure in the container at equilibrium is 5.59 atm.
I hope it helps you!
