Starting from the general expression of Kc arrive at the expression of Kp for an equilibrium established in the gas phase.
Answers
Answer:
The equilibrium constant, K_\text pK
p
K, start subscript, start text, p, end text, end subscript, describes the ratio of product and reactant concentrations at equilibrium in terms of partial pressures.
For a gas-phase reaction, \text{aA}(g)+\text{bB}(g) \leftrightharpoons \text{cC}(g)+\text{dD}(g)aA(g)+bB(g)⇋cC(g)+dD(g)start text, a, A, end text, left parenthesis, g, right parenthesis, plus, start text, b, B, end text, left parenthesis, g, right parenthesis, \leftrightharpoons, start text, c, C, end text, left parenthesis, g, right parenthesis, plus, start text, d, D, end text, left parenthesis, g, right parenthesis, the expression for K_\text pK
p
K, start subscript, start text, p, end text, end subscript is
K_\text p =\dfrac{(\text P_{\text C})^c (\text P_{\text D})^d}{(\text P_{\text A})^a (\text P_{\text B})^b}K
p
=
(P
A
)
a
(P
B
)
b
(P
C
)
c
(P
D
)
d
K, start subscript, start text, p, end text, end subscript, equals, start fraction, left parenthesis, start text, P, end text, start subscript, start text, C, end text, end subscript, right parenthesis, start superscript, c, end superscript, left parenthesis, start text, P, end text, start subscript, start text, D, end text, end subscript, right parenthesis, start superscript, d, end superscript, divided by, left parenthesis, start text, P, end text, start subscript, start text, A, end text, end subscript, right parenthesis, start superscript, a, end superscript, left parenthesis, start text, P, end text, start subscript, start text, B, end text, end subscript, right parenthesis, start superscript, b, end superscript, end fraction
K_\text pK
p
K, start subscript, start text, p, end text, end subscript is related to the equilibrium constant in terms of molar concentration, K_\text cK
c
K, start subscript, start text, c, end text, end subscript, by the equation below:
K_\text p = K_\text c(\text{RT})^{\Delta \text n}K
p
=K
c
(RT)
Δn
K, start subscript, start text, p, end text, end subscript, equals, K, start subscript, start text, c, end text, end subscript, left parenthesis, start text, R, T, end text, right parenthesis, start superscript, delta, start text, n, end text, end superscript
where \Delta \text nΔndelta, start text, n, end text is
\Delta \text n=\text{mol of product gas}-\text{mol of reactant gas}Δn=mol of product gasThe equilibrium constant, K_\text pK
p
K, start subscript, start text, p, end text, end subscript, describes the ratio of product and reactant concentrations at equilibrium in terms of partial pressures.
For a gas-phase reaction, \text{aA}(g)+\text{bB}(g) \leftrightharpoons \text{cC}(g)+\text{dD}(g)aA(g)+bB(g)⇋cC(g)+dD(g)start text, a, A, end text, left parenthesis, g, right parenthesis, plus, start text, b, B, end text, left parenthesis, g, right parenthesis, \leftrightharpoons, start text, c, C, end text, left parenthesis, g, right parenthesis, plus, start text, d, D, end text, left parenthesis, g, right parenthesis, the expression for K_\text pK
p
K, start subscript, start text, p, end text, end subscript is
K_\text p =\dfrac{(\text P_{\text C})^c (\text P_{\text D})^d}{(\text P_{\text A})^a (\text P_{\text B})^b}K
p
=
(P
A
)
a
(P
B
)
b
(P
C
)
c
(P
D
)
d
K, start subscript, start text, p, end text, end subscript, equals, start fraction, left parenthesis, start text, P, end text, start subscript, start text, C, end text, end subscript, right parenthesis, start superscript, c, end superscript, left parenthesis, start text, P, end text, start subscript, start text, D, end text, end subscript, right parenthesis, start superscript, d, end superscript, divided by, left parenthesis, start text, P, end text, start subscript, start text, A, end text, end subscript, right parenthesis, start superscript, a, end superscript, left parenthesis, start text, P, end text, start subscript, start text, B, end text, end subscript, right parenthesis, start superscript, b, end superscript, end fraction
K_\text pK
p
K, start subscript, start text, p, end text, end subscript is related to the equilibrium constant in terms of molar concentration, K_\text cK
c
K, start subscript, start text, c, end text, end subscript, by the equation below:
K_\text p = K_\text c(\text{RT})^{\Delta \text n}K
p
=K
c
(RT)
Δn
K, start subscript, start text, p, end text, end subscript, equals, K, start subscript, start text, c, end text, end subscript, left parenthesis, start text, R, T, end text, right parenthesis, start superscript, delta, start text, n, end text, end superscript
where \Delta \text nΔndelta, start text, n, end text is
\Delta \text n=\text{mol of product gas}-\text{mol of reactant gas}Δn=mol of product gas
Explanation:
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