H2SO4 + K2Cr2O7 + Na2S = H2O + K2SO4 + S + Na2SO4 + Cr2(SO4)3

Input interpretation

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sulfuric acid + potassium dichromate + sodium sulfide ⟶ water + potassium sulfate + mixed sulfur + sodium sulfate + chromium sulfate

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 + c_8 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K and Na: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_2 = c_4 + 4 c_5 + 4 c_7 + 12 c_8 S: | c_1 + c_3 = c_5 + c_6 + c_7 + 3 c_8 Cr: | 2 c_2 = 2 c_8 K: | 2 c_2 = 2 c_5 Na: | 2 c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = (3 c_1)/4 - 9/4 c_4 = c_1 c_5 = 1 c_6 = c_1 - 4 c_7 = (3 c_1)/4 - 9/4 c_8 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 7 and solve for the remaining coefficients: c_1 = 7 c_2 = 1 c_3 = 3 c_4 = 7 c_5 = 1 c_6 = 3 c_7 = 3 c_8 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 + + 3 ⟶ 7 + + 3 + 3 +