Input interpretation
H_2SO_4 sulfuric acid + MnO_2 manganese dioxide + K_2O potassium oxide ⟶ H_2O water + O_2 oxygen + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + K_2O ⟶ H_2O + O_2 + K_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 K_2O ⟶ c_4 H_2O + c_5 O_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, Mn and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_6 + c_7 Mn: | c_2 = c_7 K: | 2 c_3 = 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1 - 1 c_3 = 1 c_4 = c_1 c_5 = c_1/2 - 1/2 c_6 = 1 c_7 = c_1 - 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 3 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 MnO_2 + K_2O ⟶ 3 H_2O + O_2 + K_2SO_4 + 2 MnSO_4
Structures
+ + ⟶ + + +
Names
sulfuric acid + manganese dioxide + potassium oxide ⟶ water + oxygen + potassium sulfate + manganese(II) sulfate
Equilibrium constant
![K_c = ([H2O]^3 [O2] [K2SO4] [MnSO4]^2)/([H2SO4]^3 [MnO2]^2 [K2O])](../image_source/665f7e102459546a3b84b3239a2b34b2.png)
K_c = ([H2O]^3 [O2] [K2SO4] [MnSO4]^2)/([H2SO4]^3 [MnO2]^2 [K2O])
Rate of reaction
![rate = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = -(Δ[K2O])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/5501fdbac7aaac0f81be03909332520c.png)
rate = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = -(Δ[K2O])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | manganese dioxide | potassium oxide | water | oxygen | potassium sulfate | manganese(II) sulfate formula | H_2SO_4 | MnO_2 | K_2O | H_2O | O_2 | K_2SO_4 | MnSO_4 Hill formula | H_2O_4S | MnO_2 | K_2O | H_2O | O_2 | K_2O_4S | MnSO_4 name | sulfuric acid | manganese dioxide | potassium oxide | water | oxygen | potassium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | dioxomanganese | dipotassium oxygen(2-) | water | molecular oxygen | dipotassium sulfate | manganese(+2) cation sulfate