Question

1.

Phosphorus pentachloride is formed when phosphorus trichloride and chlorine react.

PCl_3(g) + Cl_2(g) ⇌ PCl_5(g)

The equilibrium constant for the reaction is K_C = 35.9 at 119 °C. If 0.489 mol of phosphorus trichloride is added to 0.802 mol of chlorine in a 1.08-L reaction vessel at this temperature, what is the equilibrium concentration (in mol/L) of phosphorus pentachloride?

2.

Nitric oxide is formed in automobile exhaust when nitrogen and oxygen in air react at high temperatures.

N_2(g) + O_2(g) ⇌ 2 NO_(g)

The equilibrium constant for the reaction is K_P = 0.242 at 1200 °C. If a container is charged with 0.243 atm of nitrogen and 0.101 atm of oxygen and the mixture is allowed to reach equilibrium, what will be the equilibrium partial pressure of nitrogen?

3.

Consider reaction (1) shown below with it's associated equilibrium constant. What is the equilibrium constant for reaction (2)?

Report your answer to THREE significant figures.

   (1)     A + 3 B ⇌ 2 C , K = 0.259

   (2)    2 A + 6 B ⇌ 4 C , K = ??

The pressure-based equilibrium constant for the reaction shown below is K_P = 3.575 at 443 °C. What is the value of K_C at this temperature?

2 NO_(g) + O_2(g) ⇌ 2 NO_2(g)

Answer 1

PCl_3(g) + Cl_2(g) ⇌ PCl_5(g)

Molartiy of PCl₃ = Number of moles/volume in L

Molartiy of PCl₃ = 0.489 mole/1.08 L

Molartiy of PCl₃ = 0.4528 M

Molarity of Cl₂ = Number of moles/volume in L

Molarity of Cl₂ = 0.802 mole/1.08 L

Molarity of Cl₂ = 0.7426 M

                   PCl_3(g)   +    Cl_2(g) ⇌    PCl_5(g)

I(M) 0.4528 0.7426 0

C(M) -x                  -x +x

E(M) 0.4528-x        0.7426-x +x

K_c =   [PCl₅]/[PCl₃][Cl₂]

35.9 = x/(0.4528-x)(0.7426-x)

35.9 x (0.4528-x)(0.7426-x) = x

35.9 x² - 43.915 x + 12.071 = 0

x = 0.417 M

[PCl₅] = 0.417 M

(2)

N_2(g)   +   O_2(g) ⇌ 2 NO_(g)

I(atm) 0.243 0.101 0

C(atm) -x                  -x +2x

E(atm) 0.243-x        0.101-x +2x

K_p = p²_NO/p_N2p_O2

0.242 = (2x)²/(0.243-x)(0.101-x)

0.242 = 4x²/(0.024543 - 0.344 x + x²)

3.758 x² + 0.08228 x - 0.0059394 = 0

x = 0.030 atm

p_N2 =  0.243-x =  0.243-0.03 = 0.213 atm