Question

what is the expression for the equilibrium constant for the reaction: 2 c₂h₆(g) + 7 o₂(g) ⇌ 4 co₂(g) + 6 h₂o(g)? k = \frac{co₂h₂o}{c₂h₆o₂} k = \frac{co₂^4h₂o^6}{c₂h₆^2o₂^7} k = \frac{c₂h₆o₂}{co₂h₂o} k = \frac{c₂h₆^2o₂^7}{co₂^4h₂o^6}

Explanation:

Step1: Recall the formula for equilibrium constant

For a general reaction \(aA + bB
ightleftharpoons cC + dD\), the equilibrium constant \(K=\frac{[C]^c[D]^d}{[A]^a[B]^b}\), where \([A]\), \([B]\), \([C]\), \([D]\) are the molar concentrations of \(A\), \(B\), \(C\), \(D\) respectively and \(a\), \(b\), \(c\), \(d\) are the stoichiometric coefficients.

Step2: Apply the formula to the given reaction

For the reaction \(2C_2H_6(g)+7O_2(g)
ightleftharpoons4CO_2(g)+6H_2O(g)\), \(a = 2\) (for \(C_2H_6\)), \(b = 7\) (for \(O_2\)), \(c = 4\) (for \(CO_2\)), \(d = 6\) (for \(H_2O\)).
So, \(K=\frac{[CO_2]^4[H_2O]^6}{[C_2H_6]^2[O_2]^7}\)

Answer:

\(K=\frac{[CO_2]^4[H_2O]^6}{[C_2H_6]^2[O_2]^7}\) (the second option)