HELP .. Very confused with atom economy ?

2-bromo-2-methylpropane,C4H9Br can be used to produce methylpropene,C4H8. 2-bromo-methylpropane reacts with sodium ethoxide, NaOC2H5 to produce ethanol,C2H5OH and sodium bromide , NaBr along with methylpropene. using the relative formula masses of the reactants and products,
work out the atom economy for this reaction.

What I did was i worked out the rfm of the desired product which was methylpropene,C4H8 = 56
Then I wrote down the equation b

So C4H9Br + NaOC2H5 --> C2H5OH + NaBr + C4H8

Then I added all the rfm's of all the products (C2H5OH + NaBr + C4H8)
So ((12x2) + 5 +16+1) + (23+79.9) + ((12x4)+8) = 204.9

So
atom economy = molecular mass of desired product / sum of molecular masses of all products x100

(56/204.9)x 100 = 27.3304.. So 27.3% 3s.f

Unfortunately my answer is wrong and the right answer is 41% ??

Why is that?

I do hate this atom economy stuff. There seems to be no consistency to how things are calculated.

To get 41% the maths is

Mr[C4H8]/Mr[C4H9Br]

This is really confusing, how am I supposed to know whether to use the formula of atom economy or do what you just did?

Besides why would they include the reaction of 2-bromo-methylpropane with sodium ethoxide ???

I agree with you. I'd have worked out the atom economy in the exact same way that you did.

True back of an envelope mechanism.

I do hate this atom economy stuff. There seems to be no consistency to how things are calculated.

To get 41% the maths is

Mr[C4H8]/Mr[C4H9Br]

Where is the Q from? Who says that the answer is 41%?

Whoever they are, they are wrong, it is 27.3%, even Wikipedia agrees!