Input interpretation
NaOH sodium hydroxide + MnSO_4 manganese(II) sulfate + Br_2 bromine ⟶ H_2O water + Na_2SO_4 sodium sulfate + NaBr sodium bromide + NaMnO_4 sodium permanganate
Balanced equation
Balance the chemical equation algebraically: NaOH + MnSO_4 + Br_2 ⟶ H_2O + Na_2SO_4 + NaBr + NaMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 MnSO_4 + c_3 Br_2 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 NaBr + c_7 NaMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Mn, S and Br: H: | c_1 = 2 c_4 Na: | c_1 = 2 c_5 + c_6 + c_7 O: | c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_7 Mn: | c_2 = c_7 S: | c_2 = c_5 Br: | 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 = 8 c_2 = 1 c_3 = 5/2 c_4 = 4 c_5 = 1 c_6 = 5 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 2 c_6 = 10 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 NaOH + 2 MnSO_4 + 5 Br_2 ⟶ 8 H_2O + 2 Na_2SO_4 + 10 NaBr + 2 NaMnO_4
Names
sodium hydroxide + manganese(II) sulfate + bromine ⟶ water + sodium sulfate + sodium bromide + sodium permanganate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: NaOH + MnSO_4 + Br_2 ⟶ H_2O + Na_2SO_4 + NaBr + NaMnO_4 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: 16 NaOH + 2 MnSO_4 + 5 Br_2 ⟶ 8 H_2O + 2 Na_2SO_4 + 10 NaBr + 2 NaMnO_4 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 | 16 | -16 MnSO_4 | 2 | -2 Br_2 | 5 | -5 H_2O | 8 | 8 Na_2SO_4 | 2 | 2 NaBr | 10 | 10 NaMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 16 | -16 | ([NaOH])^(-16) MnSO_4 | 2 | -2 | ([MnSO4])^(-2) Br_2 | 5 | -5 | ([Br2])^(-5) H_2O | 8 | 8 | ([H2O])^8 Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 NaBr | 10 | 10 | ([NaBr])^10 NaMnO_4 | 2 | 2 | ([NaMnO4])^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])^(-16) ([MnSO4])^(-2) ([Br2])^(-5) ([H2O])^8 ([Na2SO4])^2 ([NaBr])^10 ([NaMnO4])^2 = (([H2O])^8 ([Na2SO4])^2 ([NaBr])^10 ([NaMnO4])^2)/(([NaOH])^16 ([MnSO4])^2 ([Br2])^5)](../image_source/36d52b77bb8aec1823a5012eaafb6168.png)
Construct the equilibrium constant, K, expression for: NaOH + MnSO_4 + Br_2 ⟶ H_2O + Na_2SO_4 + NaBr + NaMnO_4 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: 16 NaOH + 2 MnSO_4 + 5 Br_2 ⟶ 8 H_2O + 2 Na_2SO_4 + 10 NaBr + 2 NaMnO_4 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 | 16 | -16 MnSO_4 | 2 | -2 Br_2 | 5 | -5 H_2O | 8 | 8 Na_2SO_4 | 2 | 2 NaBr | 10 | 10 NaMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 16 | -16 | ([NaOH])^(-16) MnSO_4 | 2 | -2 | ([MnSO4])^(-2) Br_2 | 5 | -5 | ([Br2])^(-5) H_2O | 8 | 8 | ([H2O])^8 Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 NaBr | 10 | 10 | ([NaBr])^10 NaMnO_4 | 2 | 2 | ([NaMnO4])^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])^(-16) ([MnSO4])^(-2) ([Br2])^(-5) ([H2O])^8 ([Na2SO4])^2 ([NaBr])^10 ([NaMnO4])^2 = (([H2O])^8 ([Na2SO4])^2 ([NaBr])^10 ([NaMnO4])^2)/(([NaOH])^16 ([MnSO4])^2 ([Br2])^5)
Rate of reaction
![Construct the rate of reaction expression for: NaOH + MnSO_4 + Br_2 ⟶ H_2O + Na_2SO_4 + NaBr + NaMnO_4 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: 16 NaOH + 2 MnSO_4 + 5 Br_2 ⟶ 8 H_2O + 2 Na_2SO_4 + 10 NaBr + 2 NaMnO_4 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 | 16 | -16 MnSO_4 | 2 | -2 Br_2 | 5 | -5 H_2O | 8 | 8 Na_2SO_4 | 2 | 2 NaBr | 10 | 10 NaMnO_4 | 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 | 16 | -16 | -1/16 (Δ[NaOH])/(Δt) MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) Br_2 | 5 | -5 | -1/5 (Δ[Br2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) NaBr | 10 | 10 | 1/10 (Δ[NaBr])/(Δt) NaMnO_4 | 2 | 2 | 1/2 (Δ[NaMnO4])/(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 = -1/16 (Δ[NaOH])/(Δt) = -1/2 (Δ[MnSO4])/(Δt) = -1/5 (Δ[Br2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = 1/10 (Δ[NaBr])/(Δt) = 1/2 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/0d3dd5a283f73cd7b736ee15e5460008.png)
Construct the rate of reaction expression for: NaOH + MnSO_4 + Br_2 ⟶ H_2O + Na_2SO_4 + NaBr + NaMnO_4 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: 16 NaOH + 2 MnSO_4 + 5 Br_2 ⟶ 8 H_2O + 2 Na_2SO_4 + 10 NaBr + 2 NaMnO_4 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 | 16 | -16 MnSO_4 | 2 | -2 Br_2 | 5 | -5 H_2O | 8 | 8 Na_2SO_4 | 2 | 2 NaBr | 10 | 10 NaMnO_4 | 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 | 16 | -16 | -1/16 (Δ[NaOH])/(Δt) MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) Br_2 | 5 | -5 | -1/5 (Δ[Br2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) NaBr | 10 | 10 | 1/10 (Δ[NaBr])/(Δt) NaMnO_4 | 2 | 2 | 1/2 (Δ[NaMnO4])/(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 = -1/16 (Δ[NaOH])/(Δt) = -1/2 (Δ[MnSO4])/(Δt) = -1/5 (Δ[Br2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = 1/10 (Δ[NaBr])/(Δt) = 1/2 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium hydroxide | manganese(II) sulfate | bromine | water | sodium sulfate | sodium bromide | sodium permanganate formula | NaOH | MnSO_4 | Br_2 | H_2O | Na_2SO_4 | NaBr | NaMnO_4 Hill formula | HNaO | MnSO_4 | Br_2 | H_2O | Na_2O_4S | BrNa | MnNaO_4 name | sodium hydroxide | manganese(II) sulfate | bromine | water | sodium sulfate | sodium bromide | sodium permanganate IUPAC name | sodium hydroxide | manganese(+2) cation sulfate | molecular bromine | water | disodium sulfate | sodium bromide | sodium permanganate