# Question 1c575

Sep 20, 2017

Yes, the percent yield is indeed 50%.

#### Explanation:

You know that the balanced chemical equation that describes this reaction looks like this

$2 \text{X" + 3"Y" + 4"Z" -> 5"W}$

As you can see, for every $2$ moles of $\text{X}$, the reaction consumes $3$ moles of $\text{Y}$ and $4$ moles of $\text{Z}$ and produces $5$ moles of $\text{W}$.

In your case, you start with $1$ mole of $\text{X}$, $3$ moles of $\text{Y}$, and $4$ moles of $\text{Z}$.

Right from the start, you should be able to tell that $\text{X}$ is going to act as a limiting reagent here because in order for $3$ moles of $\text{Y}$ and $4$ moles of $\text{Z}$ to react completely, you need $2$ moles of $\text{X}$.

Since you only have $1$ mole of $\text{X}$, you can say that this reactant will be the limiting reagent. This implies that it will be completely consumed before all the moles of $\text{Y}$ and of $\text{Z}$ will get the chance to take part in the reaction.

Consequently, you can say that at 100% yield, the reaction should produce

1 color(red)(cancel(color(black)("mole X"))) * overbrace("5 moles W"/(2color(red)(cancel(color(black)("moles X")))))^(color(blue)("given by the balanced chemical equation")) = "2.5 moles W"

However, you know that the reaction actually produced $1.25$ moles of $\text{W}$, which means that the percent yield of the reaction

"% yield" = "what you actually get"/"what you could theoretically get" * 100%

will be equal to

"% yield" = (1.25 color(red)(cancel(color(black)("moles W"))))/(2.5color(red)(cancel(color(black)("moles W")))) * 100% = color(darkgreen)(ul(color(black)(50%)))#