C + K2CO3 = CO + K

C activated charcoal + K_2CO_3 pearl ash ⟶ CO carbon monoxide + K potassium

Balance the chemical equation algebraically: C + K_2CO_3 ⟶ CO + K Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 K_2CO_3 ⟶ c_3 CO + c_4 K Set the number of atoms in the reactants equal to the number of atoms in the products for C, K and O: C: | c_1 + c_2 = c_3 K: | 2 c_2 = c_4 O: | 3 c_2 = c_3 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_1 = 2 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 C + K_2CO_3 ⟶ 3 CO + 2 K