H2SO4 + NaBr + Na2Cr2O7 = H2O + Na2SO4 + Br2 + Cr2(SO4)3

Input interpretation

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sulfuric acid + sodium bromide + sodium bichromate ⟶ water + sodium sulfate + bromine + chromium sulfate

Balanced equation

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Balance the chemical equation algebraically: + + ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Br, Na and Cr: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 12 c_7 S: | c_1 = c_5 + 3 c_7 Br: | c_2 = 2 c_6 Na: | c_2 + 2 c_3 = 2 c_5 Cr: | 2 c_3 = 2 c_7 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 = 7 c_2 = 6 c_3 = 1 c_4 = 7 c_5 = 4 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 + 6 + ⟶ 7 + 4 + 3 +

+ + ⟶ + + +

Names

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sulfuric acid + sodium bromide + sodium bichromate ⟶ water + sodium sulfate + bromine + chromium sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: + + ⟶ + + + 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: 7 + 6 + ⟶ 7 + 4 + 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 | 7 | -7 | 6 | -6 | 1 | -1 | 7 | 7 | 4 | 4 | 3 | 3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 7 | -7 | ([H2SO4])^(-7) | 6 | -6 | ([NaBr])^(-6) | 1 | -1 | ([Na2Cr2O7])^(-1) | 7 | 7 | ([H2O])^7 | 4 | 4 | ([Na2SO4])^4 | 3 | 3 | ([Br2])^3 | 1 | 1 | [Cr2(SO4)3] 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])^(-7) ([NaBr])^(-6) ([Na2Cr2O7])^(-1) ([H2O])^7 ([Na2SO4])^4 ([Br2])^3 [Cr2(SO4)3] = (([H2O])^7 ([Na2SO4])^4 ([Br2])^3 [Cr2(SO4)3])/(([H2SO4])^7 ([NaBr])^6 [Na2Cr2O7])

Rate of reaction

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Construct the rate of reaction expression for: + + ⟶ + + + 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: 7 + 6 + ⟶ 7 + 4 + 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 | 7 | -7 | 6 | -6 | 1 | -1 | 7 | 7 | 4 | 4 | 3 | 3 | 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) | 6 | -6 | -1/6 (Δ[NaBr])/(Δt) | 1 | -1 | -(Δ[Na2Cr2O7])/(Δt) | 7 | 7 | 1/7 (Δ[H2O])/(Δt) | 4 | 4 | 1/4 (Δ[Na2SO4])/(Δt) | 3 | 3 | 1/3 (Δ[Br2])/(Δt) | 1 | 1 | (Δ[Cr2(SO4)3])/(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 = -1/7 (Δ[H2SO4])/(Δt) = -1/6 (Δ[NaBr])/(Δt) = -(Δ[Na2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/4 (Δ[Na2SO4])/(Δt) = 1/3 (Δ[Br2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)