This problem involves calculating the equilibrium constant for COCl₂(g) ⇌ CO(g) + Cl₂(g). The equilibrium expression is Kc = [CO][Cl₂]/[COCl₂], with products in the numerator and reactant in the denominator. Substituting the equilibrium values: Kc = (0.10)(0.20)/(0.50) = 0.02/0.50 = 0.040. A student might mistakenly write the inverse expression Kc = [COCl₂]/([CO][Cl₂]) = 0.50/0.02 = 25, which gives the reciprocal of the correct answer. To avoid this error, always write the equilibrium expression for the forward reaction as given in the problem statement.

This question asks for calculating the equilibrium constant for H₂(g) + I₂(g) ⇌ 2HI(g). The equilibrium expression is Kc = [HI]²/([H₂][I₂]), where the product HI is squared because its coefficient is 2 in the balanced equation. Substituting the given concentrations: Kc = (0.80)²/((0.20)(0.20)) = 0.64/0.04 = 16. A common mistake would be to write Kc = [HI]/([H₂][I₂]) without squaring [HI], which would give 0.80/0.04 = 20, an incorrect result. Remember to always include stoichiometric coefficients as exponents in the equilibrium expression before performing calculations.

This question tests the skill of calculating the equilibrium constant. To calculate $K_c$, first write the equilibrium expression for the reaction $\mathrm{CH_3COOH(aq) \rightleftharpoons H^+(aq) + CH_3COO^-(aq)}$, which is $K_c = \frac{[\mathrm{H^+}] [\mathrm{CH_3COO^-}]}{[\mathrm{CH_3COOH}]}$. The stoichiometric coefficients become exponents in the expression, with products in the numerator and reactants in the denominator. Substitute the given equilibrium concentrations: $[\mathrm{CH_3COOH}] = 0.10, \text{M}$, $[\mathrm{H^+}] = 0.010, \text{M}$, and $[\mathrm{CH_3COO^-}] = 0.010, \text{M}$, so $K_c = (0.010 \times 0.010) / 0.10 = 0.0001 / 0.10 = 0.001 = 1.0 \times 10^{-3}$. A tempting distractor is $1.0 \times 10^{-4}$, which results from omitting the reactant concentration in the denominator. Always write the equilibrium expression based on the balanced equation first, then substitute the given equilibrium concentrations, excluding any pure solids or liquids.

This problem requires calculating the equilibrium constant for A(g) + 2B(g) ⇌ C(g). The equilibrium expression is K_c = [C]/([A][B]²), where [B] is squared because its stoichiometric coefficient is 2. Substituting the given concentrations: K_c = 0.20/((0.20)(0.10)²) = 0.20/(0.20 × 0.01) = 0.20/0.002 = 100. Choice C (0.10) represents the error of forgetting to square the B concentration, using [C]/([A][B]) instead of the correct expression. When multiple molecules of a species appear in the balanced equation, always raise that species' concentration to the corresponding power in the equilibrium expression.

This question involves calculating the equilibrium constant. For the balanced equation 2NOCl(g) ⇌ 2NO(g) + Cl₂(g), the equilibrium expression is written as products over reactants, with stoichiometric coefficients as exponents. Thus, Kc = ([NO]² [Cl₂]) / [NOCl]². Substituting the equilibrium concentrations [NOCl] = 0.20 M, [NO] = 0.20 M, and [Cl₂] = 0.05 M gives Kc = ((0.20)² × 0.05) / (0.20)² = 0.002 / 0.04 = 0.050. A tempting distractor is 0.25, which results from forgetting to square [NO], but this is incorrect because exponents are required for the coefficients. Always write the expression first, then substitute equilibrium values only—exclude pure solids and liquids.

This question asks for calculating the equilibrium constant for 2SO₂(g) + O₂(g) ⇌ 2SO₃(g). The equilibrium expression is K_c = [SO₃]²/([SO₂]²[O₂]), with both SO₃ and SO₂ concentrations squared due to their coefficients of 2. Substituting the equilibrium concentrations: K_c = (0.30)²/((0.20)²(0.10)) = 0.09/(0.04 × 0.10) = 0.09/0.004 = 22.5. Choice B (0.225) likely results from forgetting to square the concentrations, using [SO₃]/([SO₂][O₂]) instead of the correct expression with squared terms. Remember to always include stoichiometric coefficients as exponents in the equilibrium expression before performing calculations.

This problem involves calculating the equilibrium constant for H₂(g) + Br₂(g) ⇌ 2HBr(g). The equilibrium expression is K_c = [HBr]²/([H₂][Br₂]), where [HBr] is squared because its stoichiometric coefficient is 2. Substituting the given concentrations: K_c = (0.30)²/((0.30)(0.10)) = 0.09/0.03 = 3.0. Choice B (0.030) likely results from forgetting to square the HBr concentration, using [HBr]/([H₂][Br₂]) instead of [HBr]²/([H₂][Br₂]). Remember that stoichiometric coefficients become exponents in the equilibrium expression, so always check the balanced equation carefully.

This problem asks for calculating the equilibrium constant for SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g). The equilibrium expression is Kc = [SO₃][NO]/([SO₂][NO₂]), with products in the numerator and reactants in the denominator, all with exponents of 1. Substituting the concentrations: Kc = (0.10)(0.40)/((0.50)(0.20)) = 0.04/0.10 = 0.40. A typical error would be mixing up which species are products versus reactants, or perhaps calculating (0.50)(0.20)/(0.10)(0.40) = 2.5 by inverting the expression. When calculating equilibrium constants, carefully identify products and reactants from the reaction arrow, then construct your expression methodically before substituting values.

This problem involves calculating the equilibrium constant for CO₂(g) + H₂(g) ⇌ CO(g) + H₂O(g). The equilibrium expression is Kc = [CO][H₂O]/([CO₂][H₂]), with all species having exponents of 1 since all coefficients are 1. Substituting the given concentrations: Kc = (0.10)(0.20)/((0.25)(0.50)) = 0.02/0.125 = 0.16. A common mistake would be to invert the expression, calculating [CO₂][H₂]/([CO][H₂O]) = 0.125/0.02 = 6.25, which gives the reciprocal of the correct answer. When calculating equilibrium constants, always ensure products are in the numerator and reactants are in the denominator, then substitute values carefully.

This question tests the skill of calculating the equilibrium constant. To calculate K_c, first write the equilibrium expression for the reaction $ \mathrm{A(g) + 2B(g) \rightleftharpoons \mathrm{AB_2(g)} $, which is $ K_c = \frac{[\mathrm{AB_2}]}{[\mathrm{A}][\mathrm{B}]^2} $. The stoichiometric coefficients become exponents in the expression, with products in the numerator and reactants in the denominator. Substitute the given equilibrium concentrations: $[\mathrm{A}] = 0.20,\text{M}$, $[\mathrm{B}] = 0.10,\text{M}$, and $[\mathrm{AB_2}] = 0.20,\text{M}$, so $ K_c = 0.20 / (0.20 \times(0.10)^2) = 0.20 / (0.20 \times 0.01) = 0.20 / 0.002 = 100 $. A tempting distractor is 10, which results from forgetting to raise the concentration of B to the second power. Always write the equilibrium expression based on the balanced equation first, then substitute the given equilibrium concentrations, excluding any pure solids or liquids.