H2 + MnO2 = H2O2 + Mn

H_2 hydrogen + MnO_2 manganese dioxide ⟶ H_2O_2 hydrogen peroxide + Mn manganese

Balance the chemical equation algebraically: H_2 + MnO_2 ⟶ H_2O_2 + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 MnO_2 ⟶ c_3 H_2O_2 + c_4 Mn Set the number of atoms in the reactants equal to the number of atoms in the products for H, Mn and O: H: | 2 c_1 = 2 c_3 Mn: | c_2 = c_4 O: | 2 c_2 = 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_2 + MnO_2 ⟶ H_2O_2 + Mn

+ ⟶ +

hydrogen + manganese dioxide ⟶ hydrogen peroxide + manganese

Construct the equilibrium constant, K, expression for: H_2 + MnO_2 ⟶ H_2O_2 + 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: H_2 + MnO_2 ⟶ H_2O_2 + 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 H_2 | 1 | -1 MnO_2 | 1 | -1 H_2O_2 | 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 H_2 | 1 | -1 | ([H2])^(-1) MnO_2 | 1 | -1 | ([MnO2])^(-1) H_2O_2 | 1 | 1 | [H2O2] 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 = ([H2])^(-1) ([MnO2])^(-1) [H2O2] [Mn] = ([H2O2] [Mn])/([H2] [MnO2])

Construct the rate of reaction expression for: H_2 + MnO_2 ⟶ H_2O_2 + 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: H_2 + MnO_2 ⟶ H_2O_2 + 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 H_2 | 1 | -1 MnO_2 | 1 | -1 H_2O_2 | 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 H_2 | 1 | -1 | -(Δ[H2])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) H_2O_2 | 1 | 1 | (Δ[H2O2])/(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[H2])/(Δt) = -(Δ[MnO2])/(Δt) = (Δ[H2O2])/(Δt) = (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | manganese dioxide | hydrogen peroxide | manganese formula | H_2 | MnO_2 | H_2O_2 | Mn name | hydrogen | manganese dioxide | hydrogen peroxide | manganese IUPAC name | molecular hydrogen | dioxomanganese | hydrogen peroxide | manganese

| hydrogen | manganese dioxide | hydrogen peroxide | manganese molar mass | 2.016 g/mol | 86.936 g/mol | 34.014 g/mol | 54.938044 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 535 °C | -0.43 °C | 1244 °C boiling point | -252.8 °C | | 150.2 °C | 1962 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | 1.44 g/cm^3 | 7.3 g/cm^3 solubility in water | | insoluble | miscible | insoluble surface tension | | | 0.0804 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 0.001249 Pa s (at 20 °C) | odor | odorless | | |