For a general reaction aA(g) + bB(g) $⇋$ cC(g)+ dD(g), what is the relationship between the equilibrium constants $K_{c}$ and $K_{p}$ ? [assume $Δ$ n = $μ$ = (c + d) - (a+b)

$K_{p}$ = $K_{c}$ ${(R T)}^{Δ n}$

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$K_{c}$ = $K_{p}$ ${(R T)}^{- Δ n}$

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$K_{p} K_{c}$ = 1

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$K_{p}$ = $K_{c}$

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Solution

The correct option is B
$K_{c}$ = $K_{p}$ ${(R T)}^{- Δ n}$

For the reactionaA(g) + bB(g) $⇋$ cC(g) + dD(g)

$K_{p}$ = $\frac{{(P_{c})}^{c} {(P_{d})}^{d}}{{(P_{a})}^{a} {(P_{b})}^{b}}$
From Dalton's law of partial pressure,
$P_{A}$ = [A]RT; $P_{B}$ = [B]RT; $P_{C}$ = [C]RT; $P_{D}$ = [D]RT
Substituting the above in the expression for Kp, we get
$K_{p}$ = $K_{c}$ ${(R T)}^{Δ n}$ or $K_{c}$ = $K_{p}$ ${(R T)}^{- Δ n}$
where $Δ n$ = sum of coefficients of gaseous products - sum of coefficients of gaseous reactants = (c + d) - (a+b)
Hence options a and b

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For a general reaction aA(g) + bB(g) ⇋ cC(g)+ dD(g), what is the relationship between the equilibrium constants Kc and Kp? [assume Δn = μ = (c + d) - (a+b)

For a general reaction aA(g) + bB(g) $⇋$ cC(g)+ dD(g), what is the relationship between the equilibrium constants $K_{c}$ and $K_{p}$ ? [assume $Δ$ n = $μ$ = (c + d) - (a+b)