H2 + MnO2 = H2O + MnO

H_2 hydrogen + MnO_2 manganese dioxide ⟶ H_2O water + MnO manganese monoxide

Balance the chemical equation algebraically: H_2 + MnO_2 ⟶ H_2O + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 MnO_2 ⟶ c_3 H_2O + c_4 MnO 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 = c_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: | | H_2 + MnO_2 ⟶ H_2O + MnO

+ ⟶ +

hydrogen + manganese dioxide ⟶ water + manganese monoxide

| hydrogen | manganese dioxide | water | manganese monoxide molecular enthalpy | 0 kJ/mol | -520 kJ/mol | -285.8 kJ/mol | -385.2 kJ/mol total enthalpy | 0 kJ/mol | -520 kJ/mol | -285.8 kJ/mol | -385.2 kJ/mol | H_initial = -520 kJ/mol | | H_final = -671 kJ/mol | ΔH_rxn^0 | -671 kJ/mol - -520 kJ/mol = -151 kJ/mol (exothermic) | | |

| hydrogen | manganese dioxide | water | manganese monoxide molecular free energy | 0 kJ/mol | -465.1 kJ/mol | -237.1 kJ/mol | -362.9 kJ/mol total free energy | 0 kJ/mol | -465.1 kJ/mol | -237.1 kJ/mol | -362.9 kJ/mol | G_initial = -465.1 kJ/mol | | G_final = -600 kJ/mol | ΔG_rxn^0 | -600 kJ/mol - -465.1 kJ/mol = -134.9 kJ/mol (exergonic) | | |

| hydrogen | manganese dioxide | water | manganese monoxide molecular entropy | 115 J/(mol K) | 53 J/(mol K) | 69.91 J/(mol K) | 60 J/(mol K) total entropy | 115 J/(mol K) | 53 J/(mol K) | 69.91 J/(mol K) | 60 J/(mol K) | S_initial = 168 J/(mol K) | | S_final = 129.9 J/(mol K) | ΔS_rxn^0 | 129.9 J/(mol K) - 168 J/(mol K) = -38.09 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2 + MnO_2 ⟶ H_2O + MnO 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 + MnO 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 | 1 | 1 MnO | 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 | 1 | 1 | [H2O] MnO | 1 | 1 | [MnO] 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) [H2O] [MnO] = ([H2O] [MnO])/([H2] [MnO2])

Construct the rate of reaction expression for: H_2 + MnO_2 ⟶ H_2O + MnO 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 + MnO 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 | 1 | 1 MnO | 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 | 1 | 1 | (Δ[H2O])/(Δt) MnO | 1 | 1 | (Δ[MnO])/(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[H2O])/(Δt) = (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | manganese dioxide | water | manganese monoxide formula | H_2 | MnO_2 | H_2O | MnO name | hydrogen | manganese dioxide | water | manganese monoxide IUPAC name | molecular hydrogen | dioxomanganese | water | oxomanganese

| hydrogen | manganese dioxide | water | manganese monoxide molar mass | 2.016 g/mol | 86.936 g/mol | 18.015 g/mol | 70.937 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 535 °C | 0 °C | 1840 °C boiling point | -252.8 °C | | 99.9839 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | 1 g/cm^3 | 5.45 g/cm^3 solubility in water | | insoluble | | insoluble surface tension | | | 0.0728 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |