Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + CH_4 methane ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + CH_4 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 CH_4 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + 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 C: H: | 2 c_1 + 4 c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_6 + c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 C: | 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5/4 c_4 = 11/2 c_5 = 5/4 c_6 = 1 c_7 = 2 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 8 c_3 = 5 c_4 = 22 c_5 = 5 c_6 = 4 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 8 KMnO_4 + 5 CH_4 ⟶ 22 H_2O + 5 CO_2 + 4 K_2SO_4 + 8 MnSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium permanganate + methane ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate
Equilibrium constant
![K_c = ([H2O]^22 [CO2]^5 [K2SO4]^4 [MnSO4]^8)/([H2SO4]^12 [KMnO4]^8 [CH4]^5)](../image_source/467077f5d11ea379ee33b0a87072b5cc.png)
K_c = ([H2O]^22 [CO2]^5 [K2SO4]^4 [MnSO4]^8)/([H2SO4]^12 [KMnO4]^8 [CH4]^5)
Rate of reaction
![rate = -1/12 (Δ[H2SO4])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/5 (Δ[CH4])/(Δt) = 1/22 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/4 (Δ[K2SO4])/(Δt) = 1/8 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/d4fa7ff6134e25d0e23d477be0941b80.png)
rate = -1/12 (Δ[H2SO4])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -1/5 (Δ[CH4])/(Δt) = 1/22 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/4 (Δ[K2SO4])/(Δt) = 1/8 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium permanganate | methane | water | carbon dioxide | potassium sulfate | manganese(II) sulfate formula | H_2SO_4 | KMnO_4 | CH_4 | H_2O | CO_2 | K_2SO_4 | MnSO_4 Hill formula | H_2O_4S | KMnO_4 | CH_4 | H_2O | CO_2 | K_2O_4S | MnSO_4 name | sulfuric acid | potassium permanganate | methane | water | carbon dioxide | potassium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | potassium permanganate | methane | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate