Input interpretation
H_2SO_4 (sulfuric acid) + KMnO_4 (potassium permanganate) + Al (aluminum) ⟶ H_2O (water) + K_2SO_4 (potassium sulfate) + MnSO_4 (manganese(II) sulfate) + Al_2(SO_4)_3 (aluminum sulfate)
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + Al ⟶ H_2O + K_2SO_4 + MnSO_4 + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 Al ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Al: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 12 c_7 S: | c_1 = c_5 + c_6 + 3 c_7 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 Al: | c_3 = 2 c_7 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 = 8 c_2 = 2 c_3 = 10/3 c_4 = 8 c_5 = 1 c_6 = 2 c_7 = 5/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 24 c_2 = 6 c_3 = 10 c_4 = 24 c_5 = 3 c_6 = 6 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 H_2SO_4 + 6 KMnO_4 + 10 Al ⟶ 24 H_2O + 3 K_2SO_4 + 6 MnSO_4 + 5 Al_2(SO_4)_3
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium permanganate + aluminum ⟶ water + potassium sulfate + manganese(II) sulfate + aluminum sulfate
Equilibrium constant
![K_c = ([H2O]^24 [K2SO4]^3 [MnSO4]^6 [Al2(SO4)3]^5)/([H2SO4]^24 [KMnO4]^6 [Al]^10)](../image_source/6641a98207c21442192752e66d09c8ab.png)
K_c = ([H2O]^24 [K2SO4]^3 [MnSO4]^6 [Al2(SO4)3]^5)/([H2SO4]^24 [KMnO4]^6 [Al]^10)
Rate of reaction
![rate = -1/24 (Δ[H2SO4])/(Δt) = -1/6 (Δ[KMnO4])/(Δt) = -1/10 (Δ[Al])/(Δt) = 1/24 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/6 (Δ[MnSO4])/(Δt) = 1/5 (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/f098fcbd1f099717d8e13e975ddc8f1e.png)
rate = -1/24 (Δ[H2SO4])/(Δt) = -1/6 (Δ[KMnO4])/(Δt) = -1/10 (Δ[Al])/(Δt) = 1/24 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/6 (Δ[MnSO4])/(Δt) = 1/5 (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium permanganate | aluminum | water | potassium sulfate | manganese(II) sulfate | aluminum sulfate formula | H_2SO_4 | KMnO_4 | Al | H_2O | K_2SO_4 | MnSO_4 | Al_2(SO_4)_3 Hill formula | H_2O_4S | KMnO_4 | Al | H_2O | K_2O_4S | MnSO_4 | Al_2O_12S_3 name | sulfuric acid | potassium permanganate | aluminum | water | potassium sulfate | manganese(II) sulfate | aluminum sulfate IUPAC name | sulfuric acid | potassium permanganate | aluminum | water | dipotassium sulfate | manganese(+2) cation sulfate | dialuminum trisulfate