H2O + AgNO3 + H3PO2 = HNO3 + H3PO4 + Ag

Input interpretation

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H_2O water + AgNO_3 silver nitrate + H3PO2 ⟶ HNO_3 nitric acid + H_3PO_4 phosphoric acid + Ag silver

Balanced equation

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Balance the chemical equation algebraically: H_2O + AgNO_3 + H3PO2 ⟶ HNO_3 + H_3PO_4 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AgNO_3 + c_3 H3PO2 ⟶ c_4 HNO_3 + c_5 H_3PO_4 + c_6 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag, N and P: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_5 O: | c_1 + 3 c_2 + 2 c_3 = 3 c_4 + 4 c_5 Ag: | c_2 = c_6 N: | c_2 = c_4 P: | c_3 = c_5 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 = 4 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 4 AgNO_3 + H3PO2 ⟶ 4 HNO_3 + H_3PO_4 + 4 Ag

+ + H3PO2 ⟶ + +

Names

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water + silver nitrate + H3PO2 ⟶ nitric acid + phosphoric acid + silver

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + AgNO_3 + H3PO2 ⟶ HNO_3 + H_3PO_4 + Ag 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_2O + 4 AgNO_3 + H3PO2 ⟶ 4 HNO_3 + H_3PO_4 + 4 Ag 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_2O | 2 | -2 AgNO_3 | 4 | -4 H3PO2 | 1 | -1 HNO_3 | 4 | 4 H_3PO_4 | 1 | 1 Ag | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) AgNO_3 | 4 | -4 | ([AgNO3])^(-4) H3PO2 | 1 | -1 | ([H3PO2])^(-1) HNO_3 | 4 | 4 | ([HNO3])^4 H_3PO_4 | 1 | 1 | [H3PO4] Ag | 4 | 4 | ([Ag])^4 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 = ([H2O])^(-2) ([AgNO3])^(-4) ([H3PO2])^(-1) ([HNO3])^4 [H3PO4] ([Ag])^4 = (([HNO3])^4 [H3PO4] ([Ag])^4)/(([H2O])^2 ([AgNO3])^4 [H3PO2])

Rate of reaction

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Construct the rate of reaction expression for: H_2O + AgNO_3 + H3PO2 ⟶ HNO_3 + H_3PO_4 + Ag 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_2O + 4 AgNO_3 + H3PO2 ⟶ 4 HNO_3 + H_3PO_4 + 4 Ag 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_2O | 2 | -2 AgNO_3 | 4 | -4 H3PO2 | 1 | -1 HNO_3 | 4 | 4 H_3PO_4 | 1 | 1 Ag | 4 | 4 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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) AgNO_3 | 4 | -4 | -1/4 (Δ[AgNO3])/(Δt) H3PO2 | 1 | -1 | -(Δ[H3PO2])/(Δt) HNO_3 | 4 | 4 | 1/4 (Δ[HNO3])/(Δt) H_3PO_4 | 1 | 1 | (Δ[H3PO4])/(Δt) Ag | 4 | 4 | 1/4 (Δ[Ag])/(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[H2O])/(Δt) = -1/4 (Δ[AgNO3])/(Δt) = -(Δ[H3PO2])/(Δt) = 1/4 (Δ[HNO3])/(Δt) = (Δ[H3PO4])/(Δt) = 1/4 (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)