H2SO4 + K2Cr2O7 = H2O + K2SO4 + CrO3

Input interpretation

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H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + CrO_3 chromium trioxide

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + CrO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 CrO_3 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 O: | 4 c_1 + 7 c_2 = c_3 + 4 c_4 + 3 c_5 S: | c_1 = c_4 Cr: | 2 c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + 2 CrO_3

+ ⟶ + +

Names

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sulfuric acid + potassium dichromate ⟶ water + potassium sulfate + chromium trioxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + CrO_3 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: H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + 2 CrO_3 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 | 1 | -1 K_2Cr_2O_7 | 1 | -1 H_2O | 1 | 1 K_2SO_4 | 1 | 1 CrO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 1 | 1 | [H2O] K_2SO_4 | 1 | 1 | [K2SO4] CrO_3 | 2 | 2 | ([CrO3])^2 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])^(-1) ([K2Cr2O7])^(-1) [H2O] [K2SO4] ([CrO3])^2 = ([H2O] [K2SO4] ([CrO3])^2)/([H2SO4] [K2Cr2O7])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + CrO_3 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: H_2SO_4 + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + 2 CrO_3 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 | 1 | -1 K_2Cr_2O_7 | 1 | -1 H_2O | 1 | 1 K_2SO_4 | 1 | 1 CrO_3 | 2 | 2 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 | 1 | -1 | -(Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) CrO_3 | 2 | 2 | 1/2 (Δ[CrO3])/(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 = -(Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[CrO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)