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H2O + Mn3C = H2 + CH4 + Mn(OH)2

Input interpretation

H_2O water + Mn3C ⟶ H_2 hydrogen + CH_4 methane + Mn(OH)_2 manganese hydroxide
H_2O water + Mn3C ⟶ H_2 hydrogen + CH_4 methane + Mn(OH)_2 manganese hydroxide

Balanced equation

Balance the chemical equation algebraically: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Mn3C ⟶ c_3 H_2 + c_4 CH_4 + c_5 Mn(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn and C: H: | 2 c_1 = 2 c_3 + 4 c_4 + 2 c_5 O: | c_1 = 2 c_5 Mn: | 3 c_2 = c_5 C: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_2
Balance the chemical equation algebraically: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Mn3C ⟶ c_3 H_2 + c_4 CH_4 + c_5 Mn(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn and C: H: | 2 c_1 = 2 c_3 + 4 c_4 + 2 c_5 O: | c_1 = 2 c_5 Mn: | 3 c_2 = c_5 C: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_2

Structures

+ Mn3C ⟶ + +
+ Mn3C ⟶ + +

Names

water + Mn3C ⟶ hydrogen + methane + manganese hydroxide
water + Mn3C ⟶ hydrogen + methane + manganese hydroxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_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 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_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 H_2O | 6 | -6 Mn3C | 1 | -1 H_2 | 1 | 1 CH_4 | 1 | 1 Mn(OH)_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Mn3C | 1 | -1 | ([Mn3C])^(-1) H_2 | 1 | 1 | [H2] CH_4 | 1 | 1 | [CH4] Mn(OH)_2 | 3 | 3 | ([Mn(OH)2])^3 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 = ([H2O])^(-6) ([Mn3C])^(-1) [H2] [CH4] ([Mn(OH)2])^3 = ([H2] [CH4] ([Mn(OH)2])^3)/(([H2O])^6 [Mn3C])
Construct the equilibrium constant, K, expression for: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_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 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_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 H_2O | 6 | -6 Mn3C | 1 | -1 H_2 | 1 | 1 CH_4 | 1 | 1 Mn(OH)_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Mn3C | 1 | -1 | ([Mn3C])^(-1) H_2 | 1 | 1 | [H2] CH_4 | 1 | 1 | [CH4] Mn(OH)_2 | 3 | 3 | ([Mn(OH)2])^3 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 = ([H2O])^(-6) ([Mn3C])^(-1) [H2] [CH4] ([Mn(OH)2])^3 = ([H2] [CH4] ([Mn(OH)2])^3)/(([H2O])^6 [Mn3C])

Rate of reaction

Construct the rate of reaction expression for: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_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 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_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 H_2O | 6 | -6 Mn3C | 1 | -1 H_2 | 1 | 1 CH_4 | 1 | 1 Mn(OH)_2 | 3 | 3 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Mn3C | 1 | -1 | -(Δ[Mn3C])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) CH_4 | 1 | 1 | (Δ[CH4])/(Δt) Mn(OH)_2 | 3 | 3 | 1/3 (Δ[Mn(OH)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[H2O])/(Δt) = -(Δ[Mn3C])/(Δt) = (Δ[H2])/(Δt) = (Δ[CH4])/(Δt) = 1/3 (Δ[Mn(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Mn3C ⟶ H_2 + CH_4 + Mn(OH)_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 H_2O + Mn3C ⟶ H_2 + CH_4 + 3 Mn(OH)_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 H_2O | 6 | -6 Mn3C | 1 | -1 H_2 | 1 | 1 CH_4 | 1 | 1 Mn(OH)_2 | 3 | 3 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Mn3C | 1 | -1 | -(Δ[Mn3C])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) CH_4 | 1 | 1 | (Δ[CH4])/(Δt) Mn(OH)_2 | 3 | 3 | 1/3 (Δ[Mn(OH)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[H2O])/(Δt) = -(Δ[Mn3C])/(Δt) = (Δ[H2])/(Δt) = (Δ[CH4])/(Δt) = 1/3 (Δ[Mn(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | Mn3C | hydrogen | methane | manganese hydroxide formula | H_2O | Mn3C | H_2 | CH_4 | Mn(OH)_2 Hill formula | H_2O | CMn3 | H_2 | CH_4 | H_2MnO_2 name | water | | hydrogen | methane | manganese hydroxide IUPAC name | water | | molecular hydrogen | methane | manganous dihydroxide
| water | Mn3C | hydrogen | methane | manganese hydroxide formula | H_2O | Mn3C | H_2 | CH_4 | Mn(OH)_2 Hill formula | H_2O | CMn3 | H_2 | CH_4 | H_2MnO_2 name | water | | hydrogen | methane | manganese hydroxide IUPAC name | water | | molecular hydrogen | methane | manganous dihydroxide

Substance properties

| water | Mn3C | hydrogen | methane | manganese hydroxide molar mass | 18.015 g/mol | 176.825 g/mol | 2.016 g/mol | 16.04 g/mol | 88.952 g/mol phase | liquid (at STP) | | gas (at STP) | gas (at STP) | melting point | 0 °C | | -259.2 °C | -182.47 °C | boiling point | 99.9839 °C | | -252.8 °C | -161.48 °C | density | 1 g/cm^3 | | 8.99×10^-5 g/cm^3 (at 0 °C) | 6.67151×10^-4 g/cm^3 (at 20 °C) | solubility in water | | | | soluble | surface tension | 0.0728 N/m | | | 0.0137 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | 1.114×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |
| water | Mn3C | hydrogen | methane | manganese hydroxide molar mass | 18.015 g/mol | 176.825 g/mol | 2.016 g/mol | 16.04 g/mol | 88.952 g/mol phase | liquid (at STP) | | gas (at STP) | gas (at STP) | melting point | 0 °C | | -259.2 °C | -182.47 °C | boiling point | 99.9839 °C | | -252.8 °C | -161.48 °C | density | 1 g/cm^3 | | 8.99×10^-5 g/cm^3 (at 0 °C) | 6.67151×10^-4 g/cm^3 (at 20 °C) | solubility in water | | | | soluble | surface tension | 0.0728 N/m | | | 0.0137 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | 1.114×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |

Units

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