Question #1c575

1 Answer
Sep 20, 2017

Answer:

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%)))#