H2SO4 + Zn + H3PO4 = H2O + ZnSO4 + PH3

Input interpretation

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H_2SO_4 sulfuric acid + Zn zinc + H_3PO_4 phosphoric acid ⟶ H_2O water + ZnSO_4 zinc sulfate + PH_3 phosphine

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Zn + H_3PO_4 ⟶ H_2O + ZnSO_4 + PH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn + c_3 H_3PO_4 ⟶ c_4 H_2O + c_5 ZnSO_4 + c_6 PH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Zn and P: H: | 2 c_1 + 3 c_3 = 2 c_4 + 3 c_6 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 S: | c_1 = c_5 Zn: | c_2 = c_5 P: | c_3 = c_6 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 = 4 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 4 Zn + H_3PO_4 ⟶ 4 H_2O + 4 ZnSO_4 + PH_3

+ + ⟶ + +

Names

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sulfuric acid + zinc + phosphoric acid ⟶ water + zinc sulfate + phosphine

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + H_3PO_4 ⟶ H_2O + ZnSO_4 + PH_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: 4 H_2SO_4 + 4 Zn + H_3PO_4 ⟶ 4 H_2O + 4 ZnSO_4 + PH_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 | 4 | -4 Zn | 4 | -4 H_3PO_4 | 1 | -1 H_2O | 4 | 4 ZnSO_4 | 4 | 4 PH_3 | 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 | 4 | -4 | ([H2SO4])^(-4) Zn | 4 | -4 | ([Zn])^(-4) H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 ZnSO_4 | 4 | 4 | ([ZnSO4])^4 PH_3 | 1 | 1 | [PH3] 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])^(-4) ([Zn])^(-4) ([H3PO4])^(-1) ([H2O])^4 ([ZnSO4])^4 [PH3] = (([H2O])^4 ([ZnSO4])^4 [PH3])/(([H2SO4])^4 ([Zn])^4 [H3PO4])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Zn + H_3PO_4 ⟶ H_2O + ZnSO_4 + PH_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: 4 H_2SO_4 + 4 Zn + H_3PO_4 ⟶ 4 H_2O + 4 ZnSO_4 + PH_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 | 4 | -4 Zn | 4 | -4 H_3PO_4 | 1 | -1 H_2O | 4 | 4 ZnSO_4 | 4 | 4 PH_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 H_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) Zn | 4 | -4 | -1/4 (Δ[Zn])/(Δt) H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) ZnSO_4 | 4 | 4 | 1/4 (Δ[ZnSO4])/(Δt) PH_3 | 1 | 1 | (Δ[PH3])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/4 (Δ[Zn])/(Δt) = -(Δ[H3PO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[ZnSO4])/(Δt) = (Δ[PH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)