AgNO3 + Ca(H2PO4)2 = Ca(NO3)2 + AgH2PO4

Input interpretation

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AgNO_3 silver nitrate + Ca(H_2PO_4)_2·H_2O calcium dihydrogen phosphate monohydrate ⟶ Ca(NO_3)_2 calcium nitrate + AgH2PO4

Balanced equation

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Balance the chemical equation algebraically: AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + AgH2PO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 Ca(H_2PO_4)_2·H_2O ⟶ c_3 Ca(NO_3)_2 + c_4 AgH2PO4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Ca, H and P: Ag: | c_1 = c_4 N: | c_1 = 2 c_3 O: | 3 c_1 + 8 c_2 = 6 c_3 + 4 c_4 Ca: | c_2 = c_3 H: | 4 c_2 = 2 c_4 P: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + 2 AgH2PO4

+ ⟶ + AgH2PO4

Names

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silver nitrate + calcium dihydrogen phosphate monohydrate ⟶ calcium nitrate + AgH2PO4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + AgH2PO4 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 AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + 2 AgH2PO4 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 AgNO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 Ca(NO_3)_2 | 1 | 1 AgH2PO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 2 | -2 | ([AgNO3])^(-2) Ca(H_2PO_4)_2·H_2O | 1 | -1 | ([Ca(H2PO4)2·H2O])^(-1) Ca(NO_3)_2 | 1 | 1 | [Ca(NO3)2] AgH2PO4 | 2 | 2 | ([AgH2PO4])^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 = ([AgNO3])^(-2) ([Ca(H2PO4)2·H2O])^(-1) [Ca(NO3)2] ([AgH2PO4])^2 = ([Ca(NO3)2] ([AgH2PO4])^2)/(([AgNO3])^2 [Ca(H2PO4)2·H2O])

Rate of reaction

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Construct the rate of reaction expression for: AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + AgH2PO4 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 AgNO_3 + Ca(H_2PO_4)_2·H_2O ⟶ Ca(NO_3)_2 + 2 AgH2PO4 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 AgNO_3 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 Ca(NO_3)_2 | 1 | 1 AgH2PO4 | 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 AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) Ca(H_2PO_4)_2·H_2O | 1 | -1 | -(Δ[Ca(H2PO4)2·H2O])/(Δt) Ca(NO_3)_2 | 1 | 1 | (Δ[Ca(NO3)2])/(Δt) AgH2PO4 | 2 | 2 | 1/2 (Δ[AgH2PO4])/(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[AgNO3])/(Δt) = -(Δ[Ca(H2PO4)2·H2O])/(Δt) = (Δ[Ca(NO3)2])/(Δt) = 1/2 (Δ[AgH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)