H2SO4 + KMnO4 + PH3 = H2O + K2SO4 + MnSO4 + H3PO4

Input interpretation

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sulfuric acid + potassium permanganate + phosphine ⟶ water + potassium sulfate + manganese(II) sulfate + phosphoric acid

Balanced equation

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$Balance the chemical equation algebraically: + + ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and P: H: | 2 c_1 + 3 c_3 = 2 c_4 + 3 c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 P: | c_3 = c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5/4 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 5/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 8 c_3 = 5 c_4 = 12 c_5 = 4 c_6 = 8 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 + 8 + 5 ⟶ 12 + 4 + 8 + 5$

Balance the chemical equation algebraically: + + ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and P: H: | 2 c_1 + 3 c_3 = 2 c_4 + 3 c_7 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 P: | c_3 = 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 = 3 c_2 = 2 c_3 = 5/4 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 5/4 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 8 c_3 = 5 c_4 = 12 c_5 = 4 c_6 = 8 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 + 8 + 5 ⟶ 12 + 4 + 8 + 5