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H2SO4 + KMnO4 + PH3 = H2O + MnSO4 + P4 + KHSO4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + PH_3 phosphine ⟶ H_2O water + MnSO_4 manganese(II) sulfate + P_4 white phosphorus + KHSO_4 potassium bisulfate
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + PH_3 phosphine ⟶ H_2O water + MnSO_4 manganese(II) sulfate + P_4 white phosphorus + KHSO_4 potassium bisulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 PH_3 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 P_4 + c_7 KHSO_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 + 3 c_3 = 2 c_4 + c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = c_7 Mn: | c_2 = c_5 P: | c_3 = 4 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 24/5 c_2 = 12/5 c_3 = 4 c_4 = 48/5 c_5 = 12/5 c_6 = 1 c_7 = 12/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 24 c_2 = 12 c_3 = 20 c_4 = 48 c_5 = 12 c_6 = 5 c_7 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 PH_3 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 P_4 + c_7 KHSO_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 + 3 c_3 = 2 c_4 + c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = c_7 Mn: | c_2 = c_5 P: | c_3 = 4 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 24/5 c_2 = 12/5 c_3 = 4 c_4 = 48/5 c_5 = 12/5 c_6 = 1 c_7 = 12/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 24 c_2 = 12 c_3 = 20 c_4 = 48 c_5 = 12 c_6 = 5 c_7 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_4

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + phosphine ⟶ water + manganese(II) sulfate + white phosphorus + potassium bisulfate
sulfuric acid + potassium permanganate + phosphine ⟶ water + manganese(II) sulfate + white phosphorus + potassium bisulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_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: 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_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 | 24 | -24 KMnO_4 | 12 | -12 PH_3 | 20 | -20 H_2O | 48 | 48 MnSO_4 | 12 | 12 P_4 | 5 | 5 KHSO_4 | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 24 | -24 | ([H2SO4])^(-24) KMnO_4 | 12 | -12 | ([KMnO4])^(-12) PH_3 | 20 | -20 | ([PH3])^(-20) H_2O | 48 | 48 | ([H2O])^48 MnSO_4 | 12 | 12 | ([MnSO4])^12 P_4 | 5 | 5 | ([P4])^5 KHSO_4 | 12 | 12 | ([KHSO4])^12 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])^(-24) ([KMnO4])^(-12) ([PH3])^(-20) ([H2O])^48 ([MnSO4])^12 ([P4])^5 ([KHSO4])^12 = (([H2O])^48 ([MnSO4])^12 ([P4])^5 ([KHSO4])^12)/(([H2SO4])^24 ([KMnO4])^12 ([PH3])^20)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_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: 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_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 | 24 | -24 KMnO_4 | 12 | -12 PH_3 | 20 | -20 H_2O | 48 | 48 MnSO_4 | 12 | 12 P_4 | 5 | 5 KHSO_4 | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 24 | -24 | ([H2SO4])^(-24) KMnO_4 | 12 | -12 | ([KMnO4])^(-12) PH_3 | 20 | -20 | ([PH3])^(-20) H_2O | 48 | 48 | ([H2O])^48 MnSO_4 | 12 | 12 | ([MnSO4])^12 P_4 | 5 | 5 | ([P4])^5 KHSO_4 | 12 | 12 | ([KHSO4])^12 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])^(-24) ([KMnO4])^(-12) ([PH3])^(-20) ([H2O])^48 ([MnSO4])^12 ([P4])^5 ([KHSO4])^12 = (([H2O])^48 ([MnSO4])^12 ([P4])^5 ([KHSO4])^12)/(([H2SO4])^24 ([KMnO4])^12 ([PH3])^20)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_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: 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_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 | 24 | -24 KMnO_4 | 12 | -12 PH_3 | 20 | -20 H_2O | 48 | 48 MnSO_4 | 12 | 12 P_4 | 5 | 5 KHSO_4 | 12 | 12 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 | 24 | -24 | -1/24 (Δ[H2SO4])/(Δt) KMnO_4 | 12 | -12 | -1/12 (Δ[KMnO4])/(Δt) PH_3 | 20 | -20 | -1/20 (Δ[PH3])/(Δt) H_2O | 48 | 48 | 1/48 (Δ[H2O])/(Δt) MnSO_4 | 12 | 12 | 1/12 (Δ[MnSO4])/(Δt) P_4 | 5 | 5 | 1/5 (Δ[P4])/(Δt) KHSO_4 | 12 | 12 | 1/12 (Δ[KHSO4])/(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 = -1/24 (Δ[H2SO4])/(Δt) = -1/12 (Δ[KMnO4])/(Δt) = -1/20 (Δ[PH3])/(Δt) = 1/48 (Δ[H2O])/(Δt) = 1/12 (Δ[MnSO4])/(Δt) = 1/5 (Δ[P4])/(Δt) = 1/12 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + PH_3 ⟶ H_2O + MnSO_4 + P_4 + KHSO_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: 24 H_2SO_4 + 12 KMnO_4 + 20 PH_3 ⟶ 48 H_2O + 12 MnSO_4 + 5 P_4 + 12 KHSO_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 | 24 | -24 KMnO_4 | 12 | -12 PH_3 | 20 | -20 H_2O | 48 | 48 MnSO_4 | 12 | 12 P_4 | 5 | 5 KHSO_4 | 12 | 12 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 | 24 | -24 | -1/24 (Δ[H2SO4])/(Δt) KMnO_4 | 12 | -12 | -1/12 (Δ[KMnO4])/(Δt) PH_3 | 20 | -20 | -1/20 (Δ[PH3])/(Δt) H_2O | 48 | 48 | 1/48 (Δ[H2O])/(Δt) MnSO_4 | 12 | 12 | 1/12 (Δ[MnSO4])/(Δt) P_4 | 5 | 5 | 1/5 (Δ[P4])/(Δt) KHSO_4 | 12 | 12 | 1/12 (Δ[KHSO4])/(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 = -1/24 (Δ[H2SO4])/(Δt) = -1/12 (Δ[KMnO4])/(Δt) = -1/20 (Δ[PH3])/(Δt) = 1/48 (Δ[H2O])/(Δt) = 1/12 (Δ[MnSO4])/(Δt) = 1/5 (Δ[P4])/(Δt) = 1/12 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | phosphine | water | manganese(II) sulfate | white phosphorus | potassium bisulfate formula | H_2SO_4 | KMnO_4 | PH_3 | H_2O | MnSO_4 | P_4 | KHSO_4 Hill formula | H_2O_4S | KMnO_4 | H_3P | H_2O | MnSO_4 | P_4 | HKO_4S name | sulfuric acid | potassium permanganate | phosphine | water | manganese(II) sulfate | white phosphorus | potassium bisulfate IUPAC name | sulfuric acid | potassium permanganate | phosphine | water | manganese(+2) cation sulfate | tetraphosphorus | potassium hydrogen sulfate
| sulfuric acid | potassium permanganate | phosphine | water | manganese(II) sulfate | white phosphorus | potassium bisulfate formula | H_2SO_4 | KMnO_4 | PH_3 | H_2O | MnSO_4 | P_4 | KHSO_4 Hill formula | H_2O_4S | KMnO_4 | H_3P | H_2O | MnSO_4 | P_4 | HKO_4S name | sulfuric acid | potassium permanganate | phosphine | water | manganese(II) sulfate | white phosphorus | potassium bisulfate IUPAC name | sulfuric acid | potassium permanganate | phosphine | water | manganese(+2) cation sulfate | tetraphosphorus | potassium hydrogen sulfate

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