Answer
(a)
$$2COF_2(g) \leftrightharpoons CO_2(g) + CF_4(g)$$
$$K_c = \frac{[CO_2][CF_4]}{[COF_2]^2}$$
(b)
$$Cu(s) + 2Ag^{+}(aq) \leftrightharpoons Cu^{2+}(aq) + 2Ag(s)$$
$$K_c = \frac{[Cu^{2+}]}{[Ag^{+}]^2}$$
(c)
$$S_2O{_8}^{2-}(aq) + 2Fe^{2+}(aq) \leftrightharpoons 2SO{_4}^{2-}(aq) + 2Fe^{3+}(aq)$$
$$K_c = \frac{[SO{_4}^{2-}]^2[Fe^{3+}]^2}{[S_2O{_8}^{2-}][Fe^{2+}]^2}$$
Work Step by Step
1. Write and balance each reaction.
(a)
$$COF_2(g) \leftrightharpoons CO_2(g) + CF_4(g)$$
$$2COF_2(g) \leftrightharpoons CO_2(g) + CF_4(g)$$
(b)
$$Cu(s) + Ag^{+}(aq) \leftrightharpoons Cu^{2+}(aq) + Ag(s)$$
$$Cu(s) + 2Ag^{+}(aq) \leftrightharpoons Cu^{2+}(aq) + 2Ag(s)$$
(c)
$$S_2O{_8}^{2-}(aq) + Fe^{2+}(aq) \leftrightharpoons SO{_4}^{2-}(aq) + Fe^{3+}(aq)$$
$$S_2O{_8}^{2-}(aq) + 2Fe^{2+}(aq) \leftrightharpoons 2SO{_4}^{2-}(aq) + 2Fe^{3+}(aq)$$
2. The $K_c$ expression follows this pattern:
$aA + bB \leftrightharpoons cC + dD$
$$K_c =\frac{[Products]}{[Reactants]} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$
Where solids and pure liquids do not appear on the expression.
(a)
$$K_c = \frac{[CO_2][CF_4]}{[COF_2]^2}$$
(b)
$$K_c = \frac{[Cu^{2+}]}{[Ag^{+}]^2}$$
(c)
$$K_c = \frac{[SO{_4}^{2-}]^2[Fe^{3+}]^2}{[S_2O{_8}^{2-}][Fe^{2+}]^2}$$
