Input interpretation
H_2SO_4 (sulfuric acid) + Cr (chromium) ⟶ H_2O (water) + SO_2 (sulfur dioxide) + Cr_2(SO_4)_3 (chromium sulfate)
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + Cr ⟶ H_2O + SO_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cr ⟶ c_3 H_2O + c_4 SO_2 + c_5 Cr_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 and Cr: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = c_3 + 2 c_4 + 12 c_5 S: | c_1 = c_4 + 3 c_5 Cr: | c_2 = 2 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 6 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + 2 Cr ⟶ 6 H_2O + 3 SO_2 + Cr_2(SO_4)_3