H2SO4 + O2 + C12H22O11 = H2O + CO2 + SO2 + C

Input interpretation

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sulfuric acid + oxygen + sucrose ⟶ water + carbon dioxide + sulfur dioxide + activated charcoal

Balanced equation

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$Balance the chemical equation algebraically: + + ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 + c_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and C: H: | 2 c_1 + 22 c_3 = 2 c_4 O: | 4 c_1 + 2 c_2 + 11 c_3 = c_4 + 2 c_5 + 2 c_6 S: | c_1 = c_6 C: | 12 c_3 = c_5 + c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_4 = 11 c_3 + 1 c_5 = c_2 + 1/2 c_6 = 1 c_7 = -1/2 - c_2 + 12 c_3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_4 = 11 c_3 + 2 c_5 = c_2 + 1 c_6 = 2 c_7 = -1 - c_2 + 12 c_3 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_2 = 11 and c_3 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 11 c_3 = 2 c_4 = 24 c_5 = 12 c_6 = 2 c_7 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 + 11 + 2 ⟶ 24 + 12 + 2 + 12$

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 and C: H: | 2 c_1 + 22 c_3 = 2 c_4 O: | 4 c_1 + 2 c_2 + 11 c_3 = c_4 + 2 c_5 + 2 c_6 S: | c_1 = c_6 C: | 12 c_3 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_4 = 11 c_3 + 1 c_5 = c_2 + 1/2 c_6 = 1 c_7 = -1/2 - c_2 + 12 c_3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_4 = 11 c_3 + 2 c_5 = c_2 + 1 c_6 = 2 c_7 = -1 - c_2 + 12 c_3 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_2 = 11 and c_3 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 11 c_3 = 2 c_4 = 24 c_5 = 12 c_6 = 2 c_7 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 + 11 + 2 ⟶ 24 + 12 + 2 + 12