H2SO4 + CaCO3 = CaSO4 + H2CO3

H_2SO_4 sulfuric acid + CaCO_3 calcium carbonate ⟶ CaSO_4 calcium sulfate + H_2CO_3 carbonic acid

Balance the chemical equation algebraically: H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 CaCO_3 ⟶ c_3 CaSO_4 + c_4 H_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C and Ca: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = 4 c_3 + 3 c_4 S: | c_1 = c_3 C: | c_2 = c_4 Ca: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_3

+ ⟶ +

sulfuric acid + calcium carbonate ⟶ calcium sulfate + carbonic acid

Construct the equilibrium constant, K, expression for: H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_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: H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_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 | 1 | -1 CaCO_3 | 1 | -1 CaSO_4 | 1 | 1 H_2CO_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 | 1 | -1 | ([H2SO4])^(-1) CaCO_3 | 1 | -1 | ([CaCO3])^(-1) CaSO_4 | 1 | 1 | [CaSO4] H_2CO_3 | 1 | 1 | [H2CO3] 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) ([CaCO3])^(-1) [CaSO4] [H2CO3] = ([CaSO4] [H2CO3])/([H2SO4] [CaCO3])

Construct the rate of reaction expression for: H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_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: H_2SO_4 + CaCO_3 ⟶ CaSO_4 + H_2CO_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 | 1 | -1 CaCO_3 | 1 | -1 CaSO_4 | 1 | 1 H_2CO_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 | 1 | -1 | -(Δ[H2SO4])/(Δt) CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) CaSO_4 | 1 | 1 | (Δ[CaSO4])/(Δt) H_2CO_3 | 1 | 1 | (Δ[H2CO3])/(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[CaCO3])/(Δt) = (Δ[CaSO4])/(Δt) = (Δ[H2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | calcium carbonate | calcium sulfate | carbonic acid formula | H_2SO_4 | CaCO_3 | CaSO_4 | H_2CO_3 Hill formula | H_2O_4S | CCaO_3 | CaO_4S | CH_2O_3 name | sulfuric acid | calcium carbonate | calcium sulfate | carbonic acid

| sulfuric acid | calcium carbonate | calcium sulfate | carbonic acid molar mass | 98.07 g/mol | 100.09 g/mol | 136.13 g/mol | 62.024 g/mol phase | liquid (at STP) | solid (at STP) | | melting point | 10.371 °C | 1340 °C | | boiling point | 279.6 °C | | | density | 1.8305 g/cm^3 | 2.71 g/cm^3 | | solubility in water | very soluble | insoluble | slightly soluble | surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | odor | odorless | | odorless |