Mg + H2CO3 = H2 + MgCO3

Mg magnesium + H_2CO_3 carbonic acid ⟶ H_2 hydrogen + MgCO_3 magnesium carbonate

Balance the chemical equation algebraically: Mg + H_2CO_3 ⟶ H_2 + MgCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 H_2CO_3 ⟶ c_3 H_2 + c_4 MgCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, C, H and O: Mg: | c_1 = c_4 C: | c_2 = c_4 H: | 2 c_2 = 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_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: | | Mg + H_2CO_3 ⟶ H_2 + MgCO_3

+ ⟶ +

magnesium + carbonic acid ⟶ hydrogen + magnesium carbonate

Construct the equilibrium constant, K, expression for: Mg + H_2CO_3 ⟶ H_2 + MgCO_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: Mg + H_2CO_3 ⟶ H_2 + MgCO_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 Mg | 1 | -1 H_2CO_3 | 1 | -1 H_2 | 1 | 1 MgCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 1 | -1 | ([Mg])^(-1) H_2CO_3 | 1 | -1 | ([H2CO3])^(-1) H_2 | 1 | 1 | [H2] MgCO_3 | 1 | 1 | [MgCO3] 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 = ([Mg])^(-1) ([H2CO3])^(-1) [H2] [MgCO3] = ([H2] [MgCO3])/([Mg] [H2CO3])

Construct the rate of reaction expression for: Mg + H_2CO_3 ⟶ H_2 + MgCO_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: Mg + H_2CO_3 ⟶ H_2 + MgCO_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 Mg | 1 | -1 H_2CO_3 | 1 | -1 H_2 | 1 | 1 MgCO_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 Mg | 1 | -1 | -(Δ[Mg])/(Δt) H_2CO_3 | 1 | -1 | -(Δ[H2CO3])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) MgCO_3 | 1 | 1 | (Δ[MgCO3])/(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[Mg])/(Δt) = -(Δ[H2CO3])/(Δt) = (Δ[H2])/(Δt) = (Δ[MgCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | carbonic acid | hydrogen | magnesium carbonate formula | Mg | H_2CO_3 | H_2 | MgCO_3 Hill formula | Mg | CH_2O_3 | H_2 | CMgO_3 name | magnesium | carbonic acid | hydrogen | magnesium carbonate IUPAC name | magnesium | carbonic acid | molecular hydrogen | magnesium carbonate

| magnesium | carbonic acid | hydrogen | magnesium carbonate molar mass | 24.305 g/mol | 62.024 g/mol | 2.016 g/mol | 84.313 g/mol phase | solid (at STP) | | gas (at STP) | melting point | 648 °C | | -259.2 °C | boiling point | 1090 °C | | -252.8 °C | density | 1.738 g/cm^3 | | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | reacts | | | dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |