# Given the equation 2H_2O ->2H_2 + O_2, how many moles of H_2O would be required to produce 2.5 moles of O_2?

May 16, 2016

$5$ moles of ${H}_{2} O$

#### Explanation:

Since the chemical equation,

$\textcolor{red}{2} {H}_{2} O \to 2 {H}_{2} + \textcolor{b l u e}{1} {O}_{2}$

requires a specific number of moles of the reactant, then a specific number of moles of the products are created.

With this knowledge, you can create a mole ratio.

The general format of a mole ratio is as follows:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\left(\text{required based on balanced equation")/("product based on balanced equation")=("required")/("product}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, you're looking for the moles of ${H}_{2} O$ required to make $2.5$ moles of ${O}_{2}$.

Thus, your mole ratio would be:

$\frac{\textcolor{red}{2} \textcolor{w h i t e}{i} m o l \textcolor{w h i t e}{i} {H}_{2} O}{\textcolor{b l u e}{1} \textcolor{w h i t e}{i} m o l \textcolor{w h i t e}{i} {O}_{2}} = \frac{x}{2.5 \textcolor{w h i t e}{i} m o l \textcolor{w h i t e}{i} {O}_{2}}$

$\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{\Rightarrow}$where $x$ represents the moles of ${H}_{2} O$ required

From this point on, your goal is to solve for $x$ to find the moles of ${H}_{2} O$ required to produce $2.5$ moles of ${O}_{2}$.

$x = 2.5 \textcolor{p u r p \le}{\cancel{\textcolor{b l a c k}{m o l \textcolor{w h i t e}{i} {O}_{2}}}} \times \frac{2 \textcolor{w h i t e}{i} m o l \textcolor{w h i t e}{i} {H}_{2} O}{1 \textcolor{p u r p \le}{\cancel{\textcolor{b l a c k}{m o l \textcolor{w h i t e}{i} {O}_{2}}}}}$

$x = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 5 \textcolor{w h i t e}{i} m o l \textcolor{w h i t e}{i} {H}_{2} O \textcolor{w h i t e}{\frac{a}{a}} |}}}$