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We have a solution of C5H10O2 of concentration 4 M. Find out the volume we need to take from this solution to make a 250 mL solution of concentration 0.5 M.


Is my result right? I got 31.25 mL


Here's what I did:

M=moles solute / volume (L) solution (M=n/V)

First I calculate the moles of acid needed for a 0.5M, 0.25L solution.

n=MV = 0.50.25 = 0.125 mol acid

Now knowing how many moles I need to take, I calculate the volume those moles occupy in the 4M solution.

V=n/M = 0.125/4 = 0.03125 L solution = 31.25 mL

So you need to take 31.25 mL of 4M acid solution and add 218.75 (250*31.25) of water to make a 0.5M, 250 mL solution.

Verified Answer :

Hippalectryon

You are right.

Here's an easier way to do it : 
We have an initial solution of concentration \(C\).
We want to turn it into a \(V\) mL solution of concentration \(C_1\), and we want to know which volume \(V_1\) of solution to take from the original to do that.
We know that \(C_1=C\frac{V_1}V\) hence \(V_1=\frac{C_1}CV=\frac{0.5}4250=\frac{250}8=31.25 mL\)

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