Answer
The balanced equation for that combustion is:
$2 C_2H_2(g) + 5O_2(g) -^{\Delta}-\gt 4CO_2(g) +2 H_2O(g) + 2600 kJ$
Work Step by Step
1. In a combustion reaction, a carbon-containing compound reacts with oxygen gas ($O_2$) to produce carbon dioxide ($CO_2$), water $(H_2O)$ and energy in the form of heat.
Write the equation for the combustion of $C_2H_2$.
$C_2H_2(g) + O_2(g) -^{\Delta}-\gt CO_2(g) + H_2O(g) + 1300 kJ$
2. Balance the equation
a. Balance the number of carbon atoms, by putting a "2" in the front of $CO_2$:
$C_2H_2(g) + O_2(g) -^{\Delta}-\gt 2CO_2(g) + H_2O(g) + 1300 kJ$
b. The number of hydrogen atoms is already balanced.
c. Balance the number of oxygen atoms by putting a "$\frac{5}{2}$" in the front of $O_2(g)$
$C_2H_2(g) + \frac{5}{2}O_2(g) -^{\Delta}-\gt 2CO_2(g) + H_2O(g) + 1300 kJ$
3. In order to remove the fraction, we have to multiply all the coefficients and the heat by 2.
$2 C_2H_2(g) + 2 * \frac{5}{2}O_2(g) -^{\Delta}-\gt 2*2CO_2(g) +2 H_2O(g) + 2 * 1300 kJ$
$2 C_2H_2(g) + 5O_2(g) -^{\Delta}-\gt4CO_2(g) +2 H_2O(g) + 2600 kJ$