Chemistry question....overall yield?

Question

The question I have is about organic syntheses of molecules. If a synthetic route to a molecule takes 5 steps and each step is 90% efficient, what's the overall yield? One example I found was 10 steps at 80% efficiency equaling a 10% overall yield, but didn't show how this is calculated. Anyone have any ideas???

Answer 1

It's pretty simple. Just multiply the yields of each step together.

For your example: the first step gives 80%, so going into the second step you only have 80% equivalent of the starting material. After the second step, you have 80% of that, or an overall .8*.8= 64% yield. In the end, you have .8^10 yield, which is around 10-11%.

Answer 2

If the efficency is 90%, then by the first step you'll be down to 90%.

Then by the end of step 2 you'll be down to 90% of 90% (with me so far), so you could spend your time working it out. OR.

You could just do...

Overall % = (0.90)^5

It's the same thing, and you get an answer of

0.59049

This means that it will be 59% (multiply by 100 to get from decimal to %)

Hope this helps!