Input interpretation
H_2SO_4 (sulfuric acid) + MnO_2 (manganese dioxide) + KBr (potassium bromide) ⟶ H_2O (water) + K_2SO_4 (potassium sulfate) + MnSO_4 (manganese(II) sulfate) + Br_2 (bromine)
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + KBr ⟶ H_2O + K_2SO_4 + MnSO_4 + Br_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 KBr ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 Br_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mn, Br and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 + c_6 Mn: | c_2 = c_6 Br: | c_3 = 2 c_7 K: | c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + MnO_2 + 2 KBr ⟶ 2 H_2O + K_2SO_4 + MnSO_4 + Br_2
Structures
+ + ⟶ + + +
Names
sulfuric acid + manganese dioxide + potassium bromide ⟶ water + potassium sulfate + manganese(II) sulfate + bromine
Equilibrium constant
![K_c = ([H2O]^2 [K2SO4] [MnSO4] [Br2])/([H2SO4]^2 [MnO2] [KBr]^2)](../image_source/04dad48152d1f0a45f512e1c1adc5b87.png)
K_c = ([H2O]^2 [K2SO4] [MnSO4] [Br2])/([H2SO4]^2 [MnO2] [KBr]^2)
Rate of reaction
![rate = -1/2 (Δ[H2SO4])/(Δt) = -(Δ[MnO2])/(Δt) = -1/2 (Δ[KBr])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[MnSO4])/(Δt) = (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/dfd9f11f8e6d1eccd0c182f0916d992d.png)
rate = -1/2 (Δ[H2SO4])/(Δt) = -(Δ[MnO2])/(Δt) = -1/2 (Δ[KBr])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[MnSO4])/(Δt) = (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | manganese dioxide | potassium bromide | water | potassium sulfate | manganese(II) sulfate | bromine formula | H_2SO_4 | MnO_2 | KBr | H_2O | K_2SO_4 | MnSO_4 | Br_2 Hill formula | H_2O_4S | MnO_2 | BrK | H_2O | K_2O_4S | MnSO_4 | Br_2 name | sulfuric acid | manganese dioxide | potassium bromide | water | potassium sulfate | manganese(II) sulfate | bromine IUPAC name | sulfuric acid | dioxomanganese | potassium bromide | water | dipotassium sulfate | manganese(+2) cation sulfate | molecular bromine