Input interpretation
HCl (hydrogen chloride) + KMnO_4 (potassium permanganate) + K_2SO_3 (potassium sulfite) ⟶ H_2O (water) + K_2SO_4 (potassium sulfate) + KCl (potassium chloride) + MnCl_2 (manganese(II) chloride)
Balanced equation
Balance the chemical equation algebraically: HCl + KMnO_4 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KCl + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 KMnO_4 + c_3 K_2SO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KCl + c_7 MnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Mn, O and S: Cl: | c_1 = c_6 + 2 c_7 H: | c_1 = 2 c_4 K: | c_2 + 2 c_3 = 2 c_5 + c_6 Mn: | c_2 = c_7 O: | 4 c_2 + 3 c_3 = c_4 + 4 c_5 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 5/2 c_4 = 3/2 c_5 = 5/2 c_6 = 1 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 5 c_4 = 3 c_5 = 5 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 2 KMnO_4 + 5 K_2SO_3 ⟶ 3 H_2O + 5 K_2SO_4 + 2 KCl + 2 MnCl_2
Structures
+ + ⟶ + + +
Names
hydrogen chloride + potassium permanganate + potassium sulfite ⟶ water + potassium sulfate + potassium chloride + manganese(II) chloride
Equilibrium constant
![K_c = ([H2O]^3 [K2SO4]^5 [KCl]^2 [MnCl2]^2)/([HCl]^6 [KMnO4]^2 [K2SO3]^5)](../image_source/0ceae236a3dbed9bba259d898d2bb2b4.png)
K_c = ([H2O]^3 [K2SO4]^5 [KCl]^2 [MnCl2]^2)/([HCl]^6 [KMnO4]^2 [K2SO3]^5)
Rate of reaction
![rate = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[K2SO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/5 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/79a973a6e352f1b84e58e2f67cdc472f.png)
rate = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[K2SO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/5 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese(II) chloride formula | HCl | KMnO_4 | K_2SO_3 | H_2O | K_2SO_4 | KCl | MnCl_2 Hill formula | ClH | KMnO_4 | K_2O_3S | H_2O | K_2O_4S | ClK | Cl_2Mn name | hydrogen chloride | potassium permanganate | potassium sulfite | water | potassium sulfate | potassium chloride | manganese(II) chloride IUPAC name | hydrogen chloride | potassium permanganate | dipotassium sulfite | water | dipotassium sulfate | potassium chloride | dichloromanganese