Question

place the coefficients of each substance in their correct location.
ch₄ ⇌ c₂h₂ + __h₂

Explanation:

Step1: Balance carbon atoms

Let the coefficient of $CH_4$ be $a$, the coefficient of $C_2H_2$ be $b$, and the coefficient of $H_2$ be $c$. For carbon atoms, we have $a = 2b$. Let's start with $b = 1$, then $a=2$.

Step2: Balance hydrogen atoms

For hydrogen atoms, in $CH_4$ we have $4a$ hydrogen - atoms, in $C_2H_2$ we have $2b$ hydrogen - atoms, and in $H_2$ we have $2c$ hydrogen - atoms. Substituting $a = 2$ and $b = 1$ into $4a=2b + 2c$, we get $4\times2=2\times1+2c$. So $8 = 2+2c$, and $2c=6$, $c = 3$.

Answer:

$2CH_4
ightleftharpoons1C_2H_2 + 3H_2$ (coefficients are 2, 1, 3)