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NaOH + Br2 + Mn(NO3)2 = H2O + MnO2 + NaNO3 + NaBr

Input interpretation

NaOH sodium hydroxide + Br_2 bromine + Mn(NO_3)_2 manganese(II) nitrate ⟶ H_2O water + MnO_2 manganese dioxide + NaNO_3 sodium nitrate + NaBr sodium bromide
NaOH sodium hydroxide + Br_2 bromine + Mn(NO_3)_2 manganese(II) nitrate ⟶ H_2O water + MnO_2 manganese dioxide + NaNO_3 sodium nitrate + NaBr sodium bromide

Balanced equation

Balance the chemical equation algebraically: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 Mn(NO_3)_2 ⟶ c_4 H_2O + c_5 MnO_2 + c_6 NaNO_3 + c_7 NaBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br, Mn and N: H: | c_1 = 2 c_4 Na: | c_1 = c_6 + c_7 O: | c_1 + 6 c_3 = c_4 + 2 c_5 + 3 c_6 Br: | 2 c_2 = c_7 Mn: | c_3 = c_5 N: | 2 c_3 = c_6 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr
Balance the chemical equation algebraically: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 Mn(NO_3)_2 ⟶ c_4 H_2O + c_5 MnO_2 + c_6 NaNO_3 + c_7 NaBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br, Mn and N: H: | c_1 = 2 c_4 Na: | c_1 = c_6 + c_7 O: | c_1 + 6 c_3 = c_4 + 2 c_5 + 3 c_6 Br: | 2 c_2 = c_7 Mn: | c_3 = c_5 N: | 2 c_3 = c_6 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sodium hydroxide + bromine + manganese(II) nitrate ⟶ water + manganese dioxide + sodium nitrate + sodium bromide
sodium hydroxide + bromine + manganese(II) nitrate ⟶ water + manganese dioxide + sodium nitrate + sodium bromide

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr 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: 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr 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 NaOH | 4 | -4 Br_2 | 1 | -1 Mn(NO_3)_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 1 | 1 NaNO_3 | 2 | 2 NaBr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 4 | -4 | ([NaOH])^(-4) Br_2 | 1 | -1 | ([Br2])^(-1) Mn(NO_3)_2 | 1 | -1 | ([Mn(NO3)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 MnO_2 | 1 | 1 | [MnO2] NaNO_3 | 2 | 2 | ([NaNO3])^2 NaBr | 2 | 2 | ([NaBr])^2 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 = ([NaOH])^(-4) ([Br2])^(-1) ([Mn(NO3)2])^(-1) ([H2O])^2 [MnO2] ([NaNO3])^2 ([NaBr])^2 = (([H2O])^2 [MnO2] ([NaNO3])^2 ([NaBr])^2)/(([NaOH])^4 [Br2] [Mn(NO3)2])
Construct the equilibrium constant, K, expression for: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr 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: 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr 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 NaOH | 4 | -4 Br_2 | 1 | -1 Mn(NO_3)_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 1 | 1 NaNO_3 | 2 | 2 NaBr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 4 | -4 | ([NaOH])^(-4) Br_2 | 1 | -1 | ([Br2])^(-1) Mn(NO_3)_2 | 1 | -1 | ([Mn(NO3)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 MnO_2 | 1 | 1 | [MnO2] NaNO_3 | 2 | 2 | ([NaNO3])^2 NaBr | 2 | 2 | ([NaBr])^2 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 = ([NaOH])^(-4) ([Br2])^(-1) ([Mn(NO3)2])^(-1) ([H2O])^2 [MnO2] ([NaNO3])^2 ([NaBr])^2 = (([H2O])^2 [MnO2] ([NaNO3])^2 ([NaBr])^2)/(([NaOH])^4 [Br2] [Mn(NO3)2])

Rate of reaction

Construct the rate of reaction expression for: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr 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: 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr 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 NaOH | 4 | -4 Br_2 | 1 | -1 Mn(NO_3)_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 1 | 1 NaNO_3 | 2 | 2 NaBr | 2 | 2 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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) Mn(NO_3)_2 | 1 | -1 | -(Δ[Mn(NO3)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(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 = -1/4 (Δ[NaOH])/(Δt) = -(Δ[Br2])/(Δt) = -(Δ[Mn(NO3)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[MnO2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = 1/2 (Δ[NaBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + Br_2 + Mn(NO_3)_2 ⟶ H_2O + MnO_2 + NaNO_3 + NaBr 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: 4 NaOH + Br_2 + Mn(NO_3)_2 ⟶ 2 H_2O + MnO_2 + 2 NaNO_3 + 2 NaBr 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 NaOH | 4 | -4 Br_2 | 1 | -1 Mn(NO_3)_2 | 1 | -1 H_2O | 2 | 2 MnO_2 | 1 | 1 NaNO_3 | 2 | 2 NaBr | 2 | 2 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 NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) Mn(NO_3)_2 | 1 | -1 | -(Δ[Mn(NO3)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(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 = -1/4 (Δ[NaOH])/(Δt) = -(Δ[Br2])/(Δt) = -(Δ[Mn(NO3)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[MnO2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = 1/2 (Δ[NaBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | bromine | manganese(II) nitrate | water | manganese dioxide | sodium nitrate | sodium bromide formula | NaOH | Br_2 | Mn(NO_3)_2 | H_2O | MnO_2 | NaNO_3 | NaBr Hill formula | HNaO | Br_2 | MnN_2O_6 | H_2O | MnO_2 | NNaO_3 | BrNa name | sodium hydroxide | bromine | manganese(II) nitrate | water | manganese dioxide | sodium nitrate | sodium bromide IUPAC name | sodium hydroxide | molecular bromine | manganese(2+) dinitrate | water | dioxomanganese | sodium nitrate | sodium bromide
| sodium hydroxide | bromine | manganese(II) nitrate | water | manganese dioxide | sodium nitrate | sodium bromide formula | NaOH | Br_2 | Mn(NO_3)_2 | H_2O | MnO_2 | NaNO_3 | NaBr Hill formula | HNaO | Br_2 | MnN_2O_6 | H_2O | MnO_2 | NNaO_3 | BrNa name | sodium hydroxide | bromine | manganese(II) nitrate | water | manganese dioxide | sodium nitrate | sodium bromide IUPAC name | sodium hydroxide | molecular bromine | manganese(2+) dinitrate | water | dioxomanganese | sodium nitrate | sodium bromide

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