H2SO4 + Ca3(PO4)2 = CaSO4 + CaHPO4

Input interpretation

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H_2SO_4 sulfuric acid + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ CaSO_4 calcium sulfate + CaHPO_4 calcium hydrogen phosphate

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Ca_3(PO_4)_2 ⟶ CaSO_4 + CaHPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Ca_3(PO_4)_2 ⟶ c_3 CaSO_4 + c_4 CaHPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Ca and P: H: | 2 c_1 = c_4 O: | 4 c_1 + 8 c_2 = 4 c_3 + 4 c_4 S: | c_1 = c_3 Ca: | 3 c_2 = c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + Ca_3(PO_4)_2 ⟶ CaSO_4 + 2 CaHPO_4

+ ⟶ +

Names

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sulfuric acid + tricalcium diphosphate ⟶ calcium sulfate + calcium hydrogen phosphate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Ca_3(PO_4)_2 ⟶ CaSO_4 + CaHPO_4 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 + Ca_3(PO_4)_2 ⟶ CaSO_4 + 2 CaHPO_4 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 Ca_3(PO_4)_2 | 1 | -1 CaSO_4 | 1 | 1 CaHPO_4 | 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) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) CaSO_4 | 1 | 1 | [CaSO4] CaHPO_4 | 2 | 2 | ([CaHPO4])^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) ([Ca3(PO4)2])^(-1) [CaSO4] ([CaHPO4])^2 = ([CaSO4] ([CaHPO4])^2)/([H2SO4] [Ca3(PO4)2])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Ca_3(PO_4)_2 ⟶ CaSO_4 + CaHPO_4 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 + Ca_3(PO_4)_2 ⟶ CaSO_4 + 2 CaHPO_4 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 Ca_3(PO_4)_2 | 1 | -1 CaSO_4 | 1 | 1 CaHPO_4 | 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) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) CaSO_4 | 1 | 1 | (Δ[CaSO4])/(Δt) CaHPO_4 | 2 | 2 | 1/2 (Δ[CaHPO4])/(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[Ca3(PO4)2])/(Δt) = (Δ[CaSO4])/(Δt) = 1/2 (Δ[CaHPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)