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Mg + HClO3 = H2O + MgCl2 + Mg(ClO3)2

Input interpretation

Mg magnesium + HClO3 ⟶ H_2O water + MgCl_2 magnesium chloride + Mg(ClO3)2
Mg magnesium + HClO3 ⟶ H_2O water + MgCl_2 magnesium chloride + Mg(ClO3)2

Balanced equation

Balance the chemical equation algebraically: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 HClO3 ⟶ c_3 H_2O + c_4 MgCl_2 + c_5 Mg(ClO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, H, Cl and O: Mg: | c_1 = c_4 + c_5 H: | c_2 = 2 c_3 Cl: | c_2 = 2 c_4 + 2 c_5 O: | 3 c_2 = c_3 + 6 c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 12 c_3 = 6 c_4 = 1 c_5 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)2
Balance the chemical equation algebraically: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 HClO3 ⟶ c_3 H_2O + c_4 MgCl_2 + c_5 Mg(ClO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, H, Cl and O: Mg: | c_1 = c_4 + c_5 H: | c_2 = 2 c_3 Cl: | c_2 = 2 c_4 + 2 c_5 O: | 3 c_2 = c_3 + 6 c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 12 c_3 = 6 c_4 = 1 c_5 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)2

Structures

+ HClO3 ⟶ + + Mg(ClO3)2
+ HClO3 ⟶ + + Mg(ClO3)2

Names

magnesium + HClO3 ⟶ water + magnesium chloride + Mg(ClO3)2
magnesium + HClO3 ⟶ water + magnesium chloride + Mg(ClO3)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)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: 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)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 Mg | 6 | -6 HClO3 | 12 | -12 H_2O | 6 | 6 MgCl_2 | 1 | 1 Mg(ClO3)2 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 6 | -6 | ([Mg])^(-6) HClO3 | 12 | -12 | ([HClO3])^(-12) H_2O | 6 | 6 | ([H2O])^6 MgCl_2 | 1 | 1 | [MgCl2] Mg(ClO3)2 | 5 | 5 | ([Mg(ClO3)2])^5 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])^(-6) ([HClO3])^(-12) ([H2O])^6 [MgCl2] ([Mg(ClO3)2])^5 = (([H2O])^6 [MgCl2] ([Mg(ClO3)2])^5)/(([Mg])^6 ([HClO3])^12)
Construct the equilibrium constant, K, expression for: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)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: 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)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 Mg | 6 | -6 HClO3 | 12 | -12 H_2O | 6 | 6 MgCl_2 | 1 | 1 Mg(ClO3)2 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 6 | -6 | ([Mg])^(-6) HClO3 | 12 | -12 | ([HClO3])^(-12) H_2O | 6 | 6 | ([H2O])^6 MgCl_2 | 1 | 1 | [MgCl2] Mg(ClO3)2 | 5 | 5 | ([Mg(ClO3)2])^5 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])^(-6) ([HClO3])^(-12) ([H2O])^6 [MgCl2] ([Mg(ClO3)2])^5 = (([H2O])^6 [MgCl2] ([Mg(ClO3)2])^5)/(([Mg])^6 ([HClO3])^12)

Rate of reaction

Construct the rate of reaction expression for: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)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: 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)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 Mg | 6 | -6 HClO3 | 12 | -12 H_2O | 6 | 6 MgCl_2 | 1 | 1 Mg(ClO3)2 | 5 | 5 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 | 6 | -6 | -1/6 (Δ[Mg])/(Δt) HClO3 | 12 | -12 | -1/12 (Δ[HClO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) MgCl_2 | 1 | 1 | (Δ[MgCl2])/(Δt) Mg(ClO3)2 | 5 | 5 | 1/5 (Δ[Mg(ClO3)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 = -1/6 (Δ[Mg])/(Δt) = -1/12 (Δ[HClO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[MgCl2])/(Δt) = 1/5 (Δ[Mg(ClO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Mg + HClO3 ⟶ H_2O + MgCl_2 + Mg(ClO3)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: 6 Mg + 12 HClO3 ⟶ 6 H_2O + MgCl_2 + 5 Mg(ClO3)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 Mg | 6 | -6 HClO3 | 12 | -12 H_2O | 6 | 6 MgCl_2 | 1 | 1 Mg(ClO3)2 | 5 | 5 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 | 6 | -6 | -1/6 (Δ[Mg])/(Δt) HClO3 | 12 | -12 | -1/12 (Δ[HClO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) MgCl_2 | 1 | 1 | (Δ[MgCl2])/(Δt) Mg(ClO3)2 | 5 | 5 | 1/5 (Δ[Mg(ClO3)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 = -1/6 (Δ[Mg])/(Δt) = -1/12 (Δ[HClO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[MgCl2])/(Δt) = 1/5 (Δ[Mg(ClO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| magnesium | HClO3 | water | magnesium chloride | Mg(ClO3)2 formula | Mg | HClO3 | H_2O | MgCl_2 | Mg(ClO3)2 Hill formula | Mg | HClO3 | H_2O | Cl_2Mg | Cl2MgO6 name | magnesium | | water | magnesium chloride | IUPAC name | magnesium | | water | magnesium dichloride |
| magnesium | HClO3 | water | magnesium chloride | Mg(ClO3)2 formula | Mg | HClO3 | H_2O | MgCl_2 | Mg(ClO3)2 Hill formula | Mg | HClO3 | H_2O | Cl_2Mg | Cl2MgO6 name | magnesium | | water | magnesium chloride | IUPAC name | magnesium | | water | magnesium dichloride |

Substance properties

| magnesium | HClO3 | water | magnesium chloride | Mg(ClO3)2 molar mass | 24.305 g/mol | 84.45 g/mol | 18.015 g/mol | 95.2 g/mol | 191.2 g/mol phase | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 648 °C | | 0 °C | 714 °C | boiling point | 1090 °C | | 99.9839 °C | | density | 1.738 g/cm^3 | | 1 g/cm^3 | 2.32 g/cm^3 | solubility in water | reacts | | | soluble | surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |
| magnesium | HClO3 | water | magnesium chloride | Mg(ClO3)2 molar mass | 24.305 g/mol | 84.45 g/mol | 18.015 g/mol | 95.2 g/mol | 191.2 g/mol phase | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 648 °C | | 0 °C | 714 °C | boiling point | 1090 °C | | 99.9839 °C | | density | 1.738 g/cm^3 | | 1 g/cm^3 | 2.32 g/cm^3 | solubility in water | reacts | | | soluble | surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |

Units

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