HNO3 + Al = H2O + NH4NO3 + Al(NO3)3

Input interpretation

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nitric acid + aluminum ⟶ water + ammonium nitrate + aluminum nitrate

Balanced equation

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$Balance the chemical equation algebraically: + ⟶ + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 ⟶ c_3 + c_4 + c_5 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Al: H: | c_1 = 2 c_3 + 4 c_4 N: | c_1 = 2 c_4 + 3 c_5 O: | 3 c_1 = c_3 + 3 c_4 + 9 c_5 Al: | c_2 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 8/3 c_3 = 3 c_4 = 1 c_5 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 30 c_2 = 8 c_3 = 9 c_4 = 3 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 30 + 8 ⟶ 9 + 3 + 8$

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 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Al: H: | c_1 = 2 c_3 + 4 c_4 N: | c_1 = 2 c_4 + 3 c_5 O: | 3 c_1 = c_3 + 3 c_4 + 9 c_5 Al: | c_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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 8/3 c_3 = 3 c_4 = 1 c_5 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 30 c_2 = 8 c_3 = 9 c_4 = 3 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 30 + 8 ⟶ 9 + 3 + 8