HCl + MgCO3 = MgCl2 + H2CO3

HCl hydrogen chloride + MgCO_3 magnesium carbonate ⟶ MgCl_2 magnesium chloride + H_2CO_3 carbonic acid

Balance the chemical equation algebraically: HCl + MgCO_3 ⟶ MgCl_2 + H_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 MgCO_3 ⟶ c_3 MgCl_2 + c_4 H_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, C, Mg and O: Cl: | c_1 = 2 c_3 H: | c_1 = 2 c_4 C: | c_2 = c_4 Mg: | c_2 = c_3 O: | 3 c_2 = 3 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + MgCO_3 ⟶ MgCl_2 + H_2CO_3

+ ⟶ +

hydrogen chloride + magnesium carbonate ⟶ magnesium chloride + carbonic acid

Construct the equilibrium constant, K, expression for: HCl + MgCO_3 ⟶ MgCl_2 + 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: 2 HCl + MgCO_3 ⟶ MgCl_2 + 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 HCl | 2 | -2 MgCO_3 | 1 | -1 MgCl_2 | 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 HCl | 2 | -2 | ([HCl])^(-2) MgCO_3 | 1 | -1 | ([MgCO3])^(-1) MgCl_2 | 1 | 1 | [MgCl2] 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 = ([HCl])^(-2) ([MgCO3])^(-1) [MgCl2] [H2CO3] = ([MgCl2] [H2CO3])/(([HCl])^2 [MgCO3])

Construct the rate of reaction expression for: HCl + MgCO_3 ⟶ MgCl_2 + 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: 2 HCl + MgCO_3 ⟶ MgCl_2 + 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 HCl | 2 | -2 MgCO_3 | 1 | -1 MgCl_2 | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) MgCO_3 | 1 | -1 | -(Δ[MgCO3])/(Δt) MgCl_2 | 1 | 1 | (Δ[MgCl2])/(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 = -1/2 (Δ[HCl])/(Δt) = -(Δ[MgCO3])/(Δt) = (Δ[MgCl2])/(Δt) = (Δ[H2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | magnesium carbonate | magnesium chloride | carbonic acid formula | HCl | MgCO_3 | MgCl_2 | H_2CO_3 Hill formula | ClH | CMgO_3 | Cl_2Mg | CH_2O_3 name | hydrogen chloride | magnesium carbonate | magnesium chloride | carbonic acid IUPAC name | hydrogen chloride | magnesium carbonate | magnesium dichloride | carbonic acid

| hydrogen chloride | magnesium carbonate | magnesium chloride | carbonic acid molar mass | 36.46 g/mol | 84.313 g/mol | 95.2 g/mol | 62.024 g/mol phase | gas (at STP) | | solid (at STP) | melting point | -114.17 °C | | 714 °C | boiling point | -85 °C | | | density | 0.00149 g/cm^3 (at 25 °C) | | 2.32 g/cm^3 | solubility in water | miscible | | soluble |