H2SO4 + K2CrO4 = H2O + K2SO4 + H2Cr2O7

Input interpretation

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H_2SO_4 sulfuric acid + K_2CrO_4 potassium chromate ⟶ H_2O water + K_2SO_4 potassium sulfate + H_2Cr_2O_7 dichromic acid

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + H_2Cr_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2CrO_4 ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 H_2Cr_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 = 2 c_3 + 2 c_5 O: | 4 c_1 + 4 c_2 = c_3 + 4 c_4 + 7 c_5 S: | c_1 = c_4 Cr: | c_2 = 2 c_5 K: | 2 c_2 = 2 c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 K_2CrO_4 ⟶ H_2O + 2 K_2SO_4 + H_2Cr_2O_7

+ ⟶ + +

Names

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sulfuric acid + potassium chromate ⟶ water + potassium sulfate + dichromic acid

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + H_2Cr_2O_7 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 2 H_2SO_4 + 2 K_2CrO_4 ⟶ H_2O + 2 K_2SO_4 + H_2Cr_2O_7 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 2 | -2 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 2 | 2 H_2Cr_2O_7 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 1 | 1 | [H2O] K_2SO_4 | 2 | 2 | ([K2SO4])^2 H_2Cr_2O_7 | 1 | 1 | [H2Cr2O7] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-2) ([K2CrO4])^(-2) [H2O] ([K2SO4])^2 [H2Cr2O7] = ([H2O] ([K2SO4])^2 [H2Cr2O7])/(([H2SO4])^2 ([K2CrO4])^2)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + K_2CrO_4 ⟶ H_2O + K_2SO_4 + H_2Cr_2O_7 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 2 H_2SO_4 + 2 K_2CrO_4 ⟶ H_2O + 2 K_2SO_4 + H_2Cr_2O_7 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 2 | -2 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2SO_4 | 2 | 2 H_2Cr_2O_7 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) H_2Cr_2O_7 | 1 | 1 | (Δ[H2Cr2O7])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/2 (Δ[H2SO4])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = (Δ[H2Cr2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)