## General Chemistry: Principles and Modern Applications (10th Edition)

$$K' =1.1$$
1. Invert the first reaction and multiply the coefficients by 2: $$2 N_2O (g) \leftrightharpoons 2 N_2(g) + O_2(g)$$ $$K_1' = (\frac{1}{K_1})^2 = (\frac{1}{2.7 \times 10^{-8}})^2 = 1.37 \times 10^{15}$$ 2. Inver the second reaction and multiply the coefficients by 2: $$4 NO_2(g) \leftrightharpoons 2 N_2O_4(g)$$ $$K_2' = (\frac{1}{K_2})^2 = (\frac{1}{4.6 \times 10^{-3}})^2 = 4.7 \times 10^{4}$$ 3. Multiply the third reaction by 4: $$2 N_2(g) + 4 O_2(g) \leftrightharpoons 4 NO_2(g)$$ $$K_3' = (K_3)^2 = (4.1 \times 10^{-9})^2 = 1.7 \times 10^{-17}$$ 4. Sum all the new expressions, multiplying their constants $$2N_2O + 4NO_2 + 2N_2 + 4O_2 \leftrightharpoons 2N_2 + O_2 + 2 N_2O_4 + 4 NO_2$$ - Remove the repeated ones. $$2N_2O (g) + 3O_2(g) \leftrightharpoons 2 N_2O_4(g)$$ $$K' = (1.37 \times 10^{15})(4.7 \times 10^4)(1.7 \times 10^{-17}) = 1.1$$