Input interpretation
H_2SO_4 sulfuric acid + KNO_2 potassium nitrite + CaMn_2O_8 calcium permanganate ⟶ H_2O water + MnSO_4 manganese(II) sulfate + KNO_3 potassium nitrate + CaSO_4 calcium sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KNO_2 + CaMn_2O_8 ⟶ H_2O + MnSO_4 + KNO_3 + CaSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KNO_2 + c_3 CaMn_2O_8 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 KNO_3 + c_7 CaSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, N, Ca and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + 8 c_3 = c_4 + 4 c_5 + 3 c_6 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = c_6 N: | c_2 = c_6 Ca: | c_3 = c_7 Mn: | 2 c_3 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 5 c_3 = 1 c_4 = 3 c_5 = 2 c_6 = 5 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 5 KNO_2 + CaMn_2O_8 ⟶ 3 H_2O + 2 MnSO_4 + 5 KNO_3 + CaSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium nitrite + calcium permanganate ⟶ water + manganese(II) sulfate + potassium nitrate + calcium sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + KNO_2 + CaMn_2O_8 ⟶ H_2O + MnSO_4 + KNO_3 + CaSO_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: 3 H_2SO_4 + 5 KNO_2 + CaMn_2O_8 ⟶ 3 H_2O + 2 MnSO_4 + 5 KNO_3 + CaSO_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 H_2SO_4 | 3 | -3 KNO_2 | 5 | -5 CaMn_2O_8 | 1 | -1 H_2O | 3 | 3 MnSO_4 | 2 | 2 KNO_3 | 5 | 5 CaSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KNO_2 | 5 | -5 | ([KNO2])^(-5) CaMn_2O_8 | 1 | -1 | ([CaMn2O8])^(-1) H_2O | 3 | 3 | ([H2O])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 KNO_3 | 5 | 5 | ([KNO3])^5 CaSO_4 | 1 | 1 | [CaSO4] 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 = ([H2SO4])^(-3) ([KNO2])^(-5) ([CaMn2O8])^(-1) ([H2O])^3 ([MnSO4])^2 ([KNO3])^5 [CaSO4] = (([H2O])^3 ([MnSO4])^2 ([KNO3])^5 [CaSO4])/(([H2SO4])^3 ([KNO2])^5 [CaMn2O8])](../image_source/5740c58b0afa7b3a0570d2f294ae5557.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KNO_2 + CaMn_2O_8 ⟶ H_2O + MnSO_4 + KNO_3 + CaSO_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: 3 H_2SO_4 + 5 KNO_2 + CaMn_2O_8 ⟶ 3 H_2O + 2 MnSO_4 + 5 KNO_3 + CaSO_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 H_2SO_4 | 3 | -3 KNO_2 | 5 | -5 CaMn_2O_8 | 1 | -1 H_2O | 3 | 3 MnSO_4 | 2 | 2 KNO_3 | 5 | 5 CaSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) KNO_2 | 5 | -5 | ([KNO2])^(-5) CaMn_2O_8 | 1 | -1 | ([CaMn2O8])^(-1) H_2O | 3 | 3 | ([H2O])^3 MnSO_4 | 2 | 2 | ([MnSO4])^2 KNO_3 | 5 | 5 | ([KNO3])^5 CaSO_4 | 1 | 1 | [CaSO4] 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 = ([H2SO4])^(-3) ([KNO2])^(-5) ([CaMn2O8])^(-1) ([H2O])^3 ([MnSO4])^2 ([KNO3])^5 [CaSO4] = (([H2O])^3 ([MnSO4])^2 ([KNO3])^5 [CaSO4])/(([H2SO4])^3 ([KNO2])^5 [CaMn2O8])
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + KNO_2 + CaMn_2O_8 ⟶ H_2O + MnSO_4 + KNO_3 + CaSO_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: 3 H_2SO_4 + 5 KNO_2 + CaMn_2O_8 ⟶ 3 H_2O + 2 MnSO_4 + 5 KNO_3 + CaSO_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 H_2SO_4 | 3 | -3 KNO_2 | 5 | -5 CaMn_2O_8 | 1 | -1 H_2O | 3 | 3 MnSO_4 | 2 | 2 KNO_3 | 5 | 5 CaSO_4 | 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_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KNO_2 | 5 | -5 | -1/5 (Δ[KNO2])/(Δt) CaMn_2O_8 | 1 | -1 | -(Δ[CaMn2O8])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KNO_3 | 5 | 5 | 1/5 (Δ[KNO3])/(Δt) CaSO_4 | 1 | 1 | (Δ[CaSO4])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/5 (Δ[KNO2])/(Δt) = -(Δ[CaMn2O8])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[KNO3])/(Δt) = (Δ[CaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/8a47a9a78d08d44d0ce6a45abf90fed0.png)
Construct the rate of reaction expression for: H_2SO_4 + KNO_2 + CaMn_2O_8 ⟶ H_2O + MnSO_4 + KNO_3 + CaSO_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: 3 H_2SO_4 + 5 KNO_2 + CaMn_2O_8 ⟶ 3 H_2O + 2 MnSO_4 + 5 KNO_3 + CaSO_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 H_2SO_4 | 3 | -3 KNO_2 | 5 | -5 CaMn_2O_8 | 1 | -1 H_2O | 3 | 3 MnSO_4 | 2 | 2 KNO_3 | 5 | 5 CaSO_4 | 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_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) KNO_2 | 5 | -5 | -1/5 (Δ[KNO2])/(Δt) CaMn_2O_8 | 1 | -1 | -(Δ[CaMn2O8])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) KNO_3 | 5 | 5 | 1/5 (Δ[KNO3])/(Δt) CaSO_4 | 1 | 1 | (Δ[CaSO4])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/5 (Δ[KNO2])/(Δt) = -(Δ[CaMn2O8])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[KNO3])/(Δt) = (Δ[CaSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium nitrite | calcium permanganate | water | manganese(II) sulfate | potassium nitrate | calcium sulfate formula | H_2SO_4 | KNO_2 | CaMn_2O_8 | H_2O | MnSO_4 | KNO_3 | CaSO_4 Hill formula | H_2O_4S | KNO_2 | CaMn_2O_8 | H_2O | MnSO_4 | KNO_3 | CaO_4S name | sulfuric acid | potassium nitrite | calcium permanganate | water | manganese(II) sulfate | potassium nitrate | calcium sulfate IUPAC name | sulfuric acid | potassium nitrite | calcium oxido-trioxo-manganese | water | manganese(+2) cation sulfate | potassium nitrate | calcium sulfate