NaOH + CaSO4 = Na2SO4 + Ca(OH)2

Input interpretation

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NaOH sodium hydroxide + CaSO_4 calcium sulfate ⟶ Na_2SO_4 sodium sulfate + Ca(OH)_2 calcium hydroxide

Balanced equation

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Balance the chemical equation algebraically: NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 CaSO_4 ⟶ c_3 Na_2SO_4 + c_4 Ca(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Ca and S: H: | c_1 = 2 c_4 Na: | c_1 = 2 c_3 O: | c_1 + 4 c_2 = 4 c_3 + 2 c_4 Ca: | c_2 = c_4 S: | c_2 = c_3 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2

+ ⟶ +

Names

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sodium hydroxide + calcium sulfate ⟶ sodium sulfate + calcium hydroxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2 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 NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2 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 NaOH | 2 | -2 CaSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 Ca(OH)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) CaSO_4 | 1 | -1 | ([CaSO4])^(-1) Na_2SO_4 | 1 | 1 | [Na2SO4] Ca(OH)_2 | 1 | 1 | [Ca(OH)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 = ([NaOH])^(-2) ([CaSO4])^(-1) [Na2SO4] [Ca(OH)2] = ([Na2SO4] [Ca(OH)2])/(([NaOH])^2 [CaSO4])

Rate of reaction

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Construct the rate of reaction expression for: NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2 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 NaOH + CaSO_4 ⟶ Na_2SO_4 + Ca(OH)_2 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 NaOH | 2 | -2 CaSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 Ca(OH)_2 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) Ca(OH)_2 | 1 | 1 | (Δ[Ca(OH)2])/(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[NaOH])/(Δt) = -(Δ[CaSO4])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[Ca(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)