Question

Question #1c575

Answer 1

Yes, the percent yield is indeed `50%`.

Explanation:

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

`2"X" + 3"Y" + 4"Z" -> 5"W"`

As you can see, for every `2` moles of `"X"`, the reaction consumes `3` moles of `"Y"` and `4` moles of `"Z"` and produces `5` moles of `"W"`.

In your case, you start with `1` mole of `"X"`, `3` moles of `"Y"`, and `4` moles of `"Z"`.

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

Since you only have `1` mole of `"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 `"Y"` and of `"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 `"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%)))`