MnSO4 + Mg = MgSO4 + Mn

MnSO_4 manganese(II) sulfate + Mg magnesium ⟶ MgSO_4 magnesium sulfate + Mn manganese

Balance the chemical equation algebraically: MnSO_4 + Mg ⟶ MgSO_4 + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnSO_4 + c_2 Mg ⟶ c_3 MgSO_4 + c_4 Mn Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, S and Mg: Mn: | c_1 = c_4 O: | 4 c_1 = 4 c_3 S: | c_1 = c_3 Mg: | 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: | | MnSO_4 + Mg ⟶ MgSO_4 + Mn

+ ⟶ +

manganese(II) sulfate + magnesium ⟶ magnesium sulfate + manganese

Construct the equilibrium constant, K, expression for: MnSO_4 + Mg ⟶ MgSO_4 + Mn 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: MnSO_4 + Mg ⟶ MgSO_4 + Mn 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 MnSO_4 | 1 | -1 Mg | 1 | -1 MgSO_4 | 1 | 1 Mn | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnSO_4 | 1 | -1 | ([MnSO4])^(-1) Mg | 1 | -1 | ([Mg])^(-1) MgSO_4 | 1 | 1 | [MgSO4] Mn | 1 | 1 | [Mn] 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 = ([MnSO4])^(-1) ([Mg])^(-1) [MgSO4] [Mn] = ([MgSO4] [Mn])/([MnSO4] [Mg])

Construct the rate of reaction expression for: MnSO_4 + Mg ⟶ MgSO_4 + Mn 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: MnSO_4 + Mg ⟶ MgSO_4 + Mn 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 MnSO_4 | 1 | -1 Mg | 1 | -1 MgSO_4 | 1 | 1 Mn | 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 MnSO_4 | 1 | -1 | -(Δ[MnSO4])/(Δt) Mg | 1 | -1 | -(Δ[Mg])/(Δt) MgSO_4 | 1 | 1 | (Δ[MgSO4])/(Δt) Mn | 1 | 1 | (Δ[Mn])/(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[MnSO4])/(Δt) = -(Δ[Mg])/(Δt) = (Δ[MgSO4])/(Δt) = (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese(II) sulfate | magnesium | magnesium sulfate | manganese formula | MnSO_4 | Mg | MgSO_4 | Mn Hill formula | MnSO_4 | Mg | MgO_4S | Mn name | manganese(II) sulfate | magnesium | magnesium sulfate | manganese IUPAC name | manganese(+2) cation sulfate | magnesium | magnesium sulfate | manganese

| manganese(II) sulfate | magnesium | magnesium sulfate | manganese molar mass | 150.99 g/mol | 24.305 g/mol | 120.4 g/mol | 54.938044 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 710 °C | 648 °C | | 1244 °C boiling point | | 1090 °C | | 1962 °C density | 3.25 g/cm^3 | 1.738 g/cm^3 | | 7.3 g/cm^3 solubility in water | soluble | reacts | soluble | insoluble