Answer
(a) $Mg + 2HNO_3 --\gt H_2 + Mg(NO_3)_2$
(b) $CaC_2 + 2 H_2O -- \gt Ca(OH)_2 + C_2H_2$
(c) $2S + 3O_2 --\gt 2 SO_3$
(d) $UO_2 + 4HF -- \gt UF_4 + 2H_2O$
Work Step by Step
1. Identify and try to balance the elements that appear on exactly 1 compound in each side.
(a) Mg is already balanced. But nitrogen is not:
There are 2 nitrogens on the right side but only one on the left. Therefore, we should put a 2 as the coefficient of the compound with the nitrogen on the left side.
$Mg + 2HNO_3 --\gt H_2 + Mg(NO_3)_2$
(b) Calcium is already balanced, but oxygen is not.
There are 2 oxygens on the right side but only one on the left. Therefore, we should put a 2 as the coefficient of the compound with the oxygen on the left side.
$CaC_2 + 2 H_2O -- \gt Ca(OH)_2 + C_2H_2$
(c) S is already balanced. But oxygen is not:
There are 3 nitrogens on the right side, but only 2 on the left. Therefore, we should put a 3 as the coefficient of the compound with the oxygen on the left side and a 2 on the right one.
$S + 3O_2 --\gt 2 SO_3$
(d) U is already balanced. But fluorine is not:
There are 4 fluorines on the right side, but only 1 on the left. Therefore, we should put a 4 as the coefficient of the compound with the oxygen on the left side.
$UO_2 + 4HF -- \gt UF_4 + H_2O$
2. For the ones that are not balanced yet, try to balance them.
(a) Balanced.
(b) Balanced.
(c) The S is not balanced, but if we put a 2 on the sulfur on the left side, the equation will be balanced.
$2S + 3O_2 --\gt 2SO_3$
(d) The oxygen and the hydrogen aren't balanced yet. But if we put a 2 as the coefficient for $H_2O$, the equation will be totally balanced.
$UO_2 + 4HF -- \gt UF_4 + 2H_2O$
