Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + NO nitric oxide ⟶ H_2O water + K_2SO_4 potassium sulfate + NO_2 nitrogen dioxide + MnSO_4 manganese(II) sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + NO ⟶ H_2O + K_2SO_4 + NO_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 NO ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 NO_2 + c_7 MnSO_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 N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 2 c_6 + 4 c_7 S: | c_1 = c_5 + c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_7 N: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 3 c_5 = 1 c_6 = 5 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 5 NO ⟶ 3 H_2O + K_2SO_4 + 5 NO_2 + 2 MnSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium permanganate + nitric oxide ⟶ water + potassium sulfate + nitrogen dioxide + manganese(II) sulfate
Equilibrium constant
![K_c = ([H2O]^3 [K2SO4] [NO2]^5 [MnSO4]^2)/([H2SO4]^3 [KMnO4]^2 [NO]^5)](../image_source/d22020b8b5908e4ea186acbe7e72f8c1.png)
K_c = ([H2O]^3 [K2SO4] [NO2]^5 [MnSO4]^2)/([H2SO4]^3 [KMnO4]^2 [NO]^5)
Rate of reaction
![rate = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[NO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[NO2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/0e25b9a0f50948cd70b15f0b31a67ea3.png)
rate = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[NO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/5 (Δ[NO2])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium permanganate | nitric oxide | water | potassium sulfate | nitrogen dioxide | manganese(II) sulfate formula | H_2SO_4 | KMnO_4 | NO | H_2O | K_2SO_4 | NO_2 | MnSO_4 Hill formula | H_2O_4S | KMnO_4 | NO | H_2O | K_2O_4S | NO_2 | MnSO_4 name | sulfuric acid | potassium permanganate | nitric oxide | water | potassium sulfate | nitrogen dioxide | manganese(II) sulfate IUPAC name | sulfuric acid | potassium permanganate | nitric oxide | water | dipotassium sulfate | Nitrogen dioxide | manganese(+2) cation sulfate