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
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
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.
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