Question

The decomposition of solid ammonium hydrogen sulfide to form ammonia gas and hydrogen sulfide gas is an endothermic process. A 6.1589-g sample of the solid is placed in an evacuated 4.000-L vessel at 24.00˚C. After equilibrium is established, the total pressure inside the vessel is 0.709 bar and some of the solid remains in the vessel.

a. Calculate K_P for the reaction.

b. Calculate the percent of the solid that has decomposed.   

c. If the system was at equilibrium and the volume of the container were to double under isothermal conditions, what would happen to the amount of solid remaining in the vessel? Explain in mathematical terms using the reaction quotient, Q.

d. What would happen to the system at equilibrium if the temperature were to increase? Explain.

Answer 1

Nh4HS (s) = NH3(g) + H2S (g)

Moles of NH4HS= 51

Moles of NH4HS= 6.1589/51= 0.1207 moles

1 mole gives 1mole of NH3 and 1 moles of H2S = 2 moles total

0.1207 moles givs =0.1207*2= 0.2414

Pressure that would have developed upon complete decomposition

from PV= nRT

P= nRT/V= 0.2414*0.08206*(24+273.15)/ 4 =1.47 atm = 1.47*1.01325 bar =1.49 bar

Partital pressure of NH3= 1.49/2 = 0.745 atm =partial pressure of H2S

Actutal pressure =0.709 bar

1 mole of NH4HS gives 1 mole of NH3 and 1 mole of H2S

at equilibrium the the total pressure inside the veseel is 0.709 bar

let x= partial pressure of NH3 and hence x= parial presssure of H2S

Total pressure = 2x= 0.709    x= 0.709/2 = 0.3545 bar

complete solid decompostion gives rise to a pressure of 1.49

but the pressure was =0.709 bar

% decomposed = (0.709/1.49)*100= 47.48%

When the volume of the vessel gets doubled underisothermal cndition, pressure also gets doubled. The new pressure becomes =1.49*2= 2.98 atm

% decomposition = 100*(0.709/2.98)=23.78%

As per Lechatlier principlle, the increase in pressure takes the reaction to a directino of decrease in number of moles, i.e backward direction and this is justifed.

When temperature increases, the reaction proceeds in a direction to compensate the effect of temperature, decrease in temperature. Hence backward direction is preferred.