Question

The reaction

C(s)+2H2(g)⇌CH4(g)

has Kp=0.263 at 1000. K. Calculate the total pressure at equilibrium when 5.759 g of H2 and 22.94 g of C(s) are placed in a 9.88 L flask and heated to 1000. K.

Ptotal= ? atm

Calculate the total pressure when 5.759 g

of H2 and 8.755 g of C(s) are placed in a 9.88 L flask and heated to 1000. K.

Ptotal= ? atm

Answer 1

given chemical reaction is  

C(s) + 2H2(g) --> CH4(g)

Equilibrium constant (Kp) is the ratio between the product of partial pressure of products, each raised to the number of moles involved to product of partial pressure of reactants, each raised to the number of moles involved, present at equilibrium. Thee partial pressure are the partial pressure of gases only.

The partial pressure of pure solid and liquid are always 1.

So for the given reaction,

Kp = PCH4 / PH2(g)2

where

• PCH4 = Partial pressure of CH4
• PH2 = Partial pressure of H2(g)

Again total pressure of a system is the sum of partial pressure of all the gases present.

i.e Ptot = PCH4 + PH2

a-

mass of H2 taken = 5.759 g

So moles of H2 taken = mass / molar mass

= 5.759 g / 2 g/mol

= 2.8795‬ moles

So partial pressure of H2 can be calculated from the ideal gas equation PV = nRT

Putting the values

PV = nRT

PH2 * 9.88L = 2.8795‬ mols * (0.0821 L.atm/mol.K) * 1000K

PH2 * 9.88L = 184.25 L.atm

PH2 = 236.41 L.atm / 9.88L

= 23.93 atm

Similarly-

given mass of C(s) taken = 22.94 g

So moles of C(s) taken = mass / molar mass

= 22.94 g / 12 g/mol

= 1.9‬12 moles

for pressure calculation we have nothing to do with pure solids. So the ICE table will be-

Reaction	PH2 (for 2H2)	PCH4
Initial	23.93 atm	0
Change	-2x	+x
Equilibrium	23.93 atm-2x	x

So putting the values in-

Kp = PCH4 / PH2(g)2

0.263 = x / (23.93 atm-2x)2

0.263 * (23.93 atm-2x)2 = x

0.263 * (572.64 - 95.72x + 4x2) = x

150.60 - 25.70‬x + 1.052x2) = x

1.052x2 - 25.70x - x + 150.60 = 0

1.052x2 -26.70x + 150.60 = 0

solving this,

x = 8.46

So putting this value, at equilibrium

PCH4 = x = 8.46 atm

PH2 = 23.93 atm-2x = 23.93 atm - (2*8.46) atm = 23.93 atm - 16.92 atm = 7.01‬ atm

So at equilibrium,

Ptot = PCH4 + PH2

= 8.46 atm + 7.01 atm

= 15.47 atm

b-

also the mass of H2 remains the same, only that of solid C changes, which don't have any effect on total pressure. So the total pressure remains the same.