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H2SO4 + KMnO4 + P2H4 = H2O + K2SO4 + MnSO4 + H3PO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_4P_2 diphosphine ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + H_3PO_4 phosphoric acid
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_4P_2 diphosphine ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + H_3PO_4 phosphoric acid

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_4P_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and P: H: | 2 c_1 + 4 c_3 = 2 c_4 + 3 c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 P: | 2 c_3 = c_7 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 = 21/5 c_2 = 14/5 c_3 = 1 c_4 = 16/5 c_5 = 7/5 c_6 = 14/5 c_7 = 2 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 21 c_2 = 14 c_3 = 5 c_4 = 16 c_5 = 7 c_6 = 14 c_7 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_4P_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and P: H: | 2 c_1 + 4 c_3 = 2 c_4 + 3 c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 P: | 2 c_3 = c_7 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 = 21/5 c_2 = 14/5 c_3 = 1 c_4 = 16/5 c_5 = 7/5 c_6 = 14/5 c_7 = 2 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 21 c_2 = 14 c_3 = 5 c_4 = 16 c_5 = 7 c_6 = 14 c_7 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_4

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + diphosphine ⟶ water + potassium sulfate + manganese(II) sulfate + phosphoric acid
sulfuric acid + potassium permanganate + diphosphine ⟶ water + potassium sulfate + manganese(II) sulfate + phosphoric acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_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: 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_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 | 21 | -21 KMnO_4 | 14 | -14 H_4P_2 | 5 | -5 H_2O | 16 | 16 K_2SO_4 | 7 | 7 MnSO_4 | 14 | 14 H_3PO_4 | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 21 | -21 | ([H2SO4])^(-21) KMnO_4 | 14 | -14 | ([KMnO4])^(-14) H_4P_2 | 5 | -5 | ([H4P2])^(-5) H_2O | 16 | 16 | ([H2O])^16 K_2SO_4 | 7 | 7 | ([K2SO4])^7 MnSO_4 | 14 | 14 | ([MnSO4])^14 H_3PO_4 | 10 | 10 | ([H3PO4])^10 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])^(-21) ([KMnO4])^(-14) ([H4P2])^(-5) ([H2O])^16 ([K2SO4])^7 ([MnSO4])^14 ([H3PO4])^10 = (([H2O])^16 ([K2SO4])^7 ([MnSO4])^14 ([H3PO4])^10)/(([H2SO4])^21 ([KMnO4])^14 ([H4P2])^5)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_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: 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_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 | 21 | -21 KMnO_4 | 14 | -14 H_4P_2 | 5 | -5 H_2O | 16 | 16 K_2SO_4 | 7 | 7 MnSO_4 | 14 | 14 H_3PO_4 | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 21 | -21 | ([H2SO4])^(-21) KMnO_4 | 14 | -14 | ([KMnO4])^(-14) H_4P_2 | 5 | -5 | ([H4P2])^(-5) H_2O | 16 | 16 | ([H2O])^16 K_2SO_4 | 7 | 7 | ([K2SO4])^7 MnSO_4 | 14 | 14 | ([MnSO4])^14 H_3PO_4 | 10 | 10 | ([H3PO4])^10 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])^(-21) ([KMnO4])^(-14) ([H4P2])^(-5) ([H2O])^16 ([K2SO4])^7 ([MnSO4])^14 ([H3PO4])^10 = (([H2O])^16 ([K2SO4])^7 ([MnSO4])^14 ([H3PO4])^10)/(([H2SO4])^21 ([KMnO4])^14 ([H4P2])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_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: 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_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 | 21 | -21 KMnO_4 | 14 | -14 H_4P_2 | 5 | -5 H_2O | 16 | 16 K_2SO_4 | 7 | 7 MnSO_4 | 14 | 14 H_3PO_4 | 10 | 10 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 | 21 | -21 | -1/21 (Δ[H2SO4])/(Δt) KMnO_4 | 14 | -14 | -1/14 (Δ[KMnO4])/(Δt) H_4P_2 | 5 | -5 | -1/5 (Δ[H4P2])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) K_2SO_4 | 7 | 7 | 1/7 (Δ[K2SO4])/(Δt) MnSO_4 | 14 | 14 | 1/14 (Δ[MnSO4])/(Δt) H_3PO_4 | 10 | 10 | 1/10 (Δ[H3PO4])/(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 = -1/21 (Δ[H2SO4])/(Δt) = -1/14 (Δ[KMnO4])/(Δt) = -1/5 (Δ[H4P2])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/7 (Δ[K2SO4])/(Δt) = 1/14 (Δ[MnSO4])/(Δt) = 1/10 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_4P_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + H_3PO_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: 21 H_2SO_4 + 14 KMnO_4 + 5 H_4P_2 ⟶ 16 H_2O + 7 K_2SO_4 + 14 MnSO_4 + 10 H_3PO_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 | 21 | -21 KMnO_4 | 14 | -14 H_4P_2 | 5 | -5 H_2O | 16 | 16 K_2SO_4 | 7 | 7 MnSO_4 | 14 | 14 H_3PO_4 | 10 | 10 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 | 21 | -21 | -1/21 (Δ[H2SO4])/(Δt) KMnO_4 | 14 | -14 | -1/14 (Δ[KMnO4])/(Δt) H_4P_2 | 5 | -5 | -1/5 (Δ[H4P2])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) K_2SO_4 | 7 | 7 | 1/7 (Δ[K2SO4])/(Δt) MnSO_4 | 14 | 14 | 1/14 (Δ[MnSO4])/(Δt) H_3PO_4 | 10 | 10 | 1/10 (Δ[H3PO4])/(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 = -1/21 (Δ[H2SO4])/(Δt) = -1/14 (Δ[KMnO4])/(Δt) = -1/5 (Δ[H4P2])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/7 (Δ[K2SO4])/(Δt) = 1/14 (Δ[MnSO4])/(Δt) = 1/10 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | diphosphine | water | potassium sulfate | manganese(II) sulfate | phosphoric acid formula | H_2SO_4 | KMnO_4 | H_4P_2 | H_2O | K_2SO_4 | MnSO_4 | H_3PO_4 Hill formula | H_2O_4S | KMnO_4 | H_4P_2 | H_2O | K_2O_4S | MnSO_4 | H_3O_4P name | sulfuric acid | potassium permanganate | diphosphine | water | potassium sulfate | manganese(II) sulfate | phosphoric acid IUPAC name | sulfuric acid | potassium permanganate | phosphinophosphine | water | dipotassium sulfate | manganese(+2) cation sulfate | phosphoric acid
| sulfuric acid | potassium permanganate | diphosphine | water | potassium sulfate | manganese(II) sulfate | phosphoric acid formula | H_2SO_4 | KMnO_4 | H_4P_2 | H_2O | K_2SO_4 | MnSO_4 | H_3PO_4 Hill formula | H_2O_4S | KMnO_4 | H_4P_2 | H_2O | K_2O_4S | MnSO_4 | H_3O_4P name | sulfuric acid | potassium permanganate | diphosphine | water | potassium sulfate | manganese(II) sulfate | phosphoric acid IUPAC name | sulfuric acid | potassium permanganate | phosphinophosphine | water | dipotassium sulfate | manganese(+2) cation sulfate | phosphoric acid

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