Input interpretation
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + CH_3C congruent CH methylacetylene ⟶ H_2O water + CO_2 carbon dioxide + KOH potassium hydroxide + MnSO_4 manganese(II) sulfate + CH_3CO_2H acetic acid
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + CH_3C congruent CH ⟶ H_2O + CO_2 + KOH + MnSO_4 + CH_3CO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 CH_3C congruent CH ⟶ c_4 H_2O + c_5 CO_2 + c_6 KOH + c_7 MnSO_4 + c_8 CH_3CO_2H 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 + c_6 + 4 c_8 O: | 4 c_1 + 4 c_2 = c_4 + 2 c_5 + c_6 + 4 c_7 + 2 c_8 S: | c_1 = c_7 K: | c_2 = c_6 Mn: | c_2 = c_7 C: | 3 c_3 = c_5 + 2 c_8 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1 c_3 = (7 c_1)/8 - 1/2 c_4 = 1 c_5 = (3 c_1)/8 + 1/2 c_6 = c_1 c_7 = c_1 c_8 = (9 c_1)/8 - 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_2 = c_1 c_3 = (7 c_1)/8 - 2 c_4 = 4 c_5 = (3 c_1)/8 + 2 c_6 = c_1 c_7 = c_1 c_8 = (9 c_1)/8 - 4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 8 and solve for the remaining coefficients: c_1 = 8 c_2 = 8 c_3 = 5 c_4 = 4 c_5 = 5 c_6 = 8 c_7 = 8 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 H_2SO_4 + 8 KMnO_4 + 5 CH_3C congruent CH ⟶ 4 H_2O + 5 CO_2 + 8 KOH + 8 MnSO_4 + 5 CH_3CO_2H
Structures
+ + ⟶ + + + +
Names
sulfuric acid + potassium permanganate + methylacetylene ⟶ water + carbon dioxide + potassium hydroxide + manganese(II) sulfate + acetic acid