Calculating Buffer Volumes for pH and Concentration Ratios

[jsmith613]

Homework Statement

An buffer is made from a 0.1M acid and a 0.25 M salt.
According to the equation
pH = pK_a - log[acid]/[base]
the ratio acid:base is 1:2

What volumes are required to make a 1 dm³ solution?

Homework Equations

The Attempt at a Solution

According to the 1:2 ratio we would need
333.3 cm³ of acid and 666.6 cm³ of base
However as the initial concentration of acid to base is 0.1:0.25 we instead say
volume acid = 333.3cm³
volume base = 666.6 cm³/2.5 = 266.6 cm³
volume water = 400 cm³

(all of these volumes are rounded to the nearest 0.1 cm³)

is this correct?

 

[Borek]

Question doesn't say anything about using additional water for dilution, so I don't think that's the correct answer.

 

[jsmith613]

yes but as I need to make up a litre the rest of the solution must be water

 

[Borek]

No, you don't have to add water. If you mix correct volumes of both solutions you will have a liter of solution with a correct ratio of acid and conjugate base. Try to write two equations describing both ratio and volume - that will give you two equations in two unknowns, easy to solve.

 

[jsmith613]

666.67 cm³ acid
and
333.333 cm^3[/base]

 

[Borek]

Have you checked if the ratio is correct if you use these volumes?

 

[jsmith613]

ratio acid:base assuming 1M:1M initial ratio gives 1:2
BUT initial molar ratio is 1:2.5
therefore new acid:base ratio from pH = pKa - log[acid]/[base] is 1:(2/2.5) = 1:0.8
...oh
acid: 555.6 cm³
base: 444.4 cm³

right?

 

[Borek]

Sorry, we are not checking homework, we are helping solve it.

 

[jsmith613]

This is not homework
this is a revision question I can't find an answer to
am i right?