[student8607]

I am to designer a buffer for
0.01M H₂PO₄^-/HPO₄^2- buffer with a pH of 7.2

STEP #1 determine ratio of HPO₄^2- to H₂PO₄^-

HPO₄^2- / H₂PO₄^- = Ka/H+

The Ka is given at 6.2 x 10^-8
my H+ is 6.31 x 10^-8

so: HPO₄^2- = 0.983 x H₂PO₄^-


STEP #2. determine individual concentrations

HPO₄^2- = 0.983 x H₂PO₄^- and HPO₄^2- + H₂PO₄^- = 0.01M

0.983 x H₂PO₄^- + H₂PO₄^- = 0.01

how am I to solve for the individual concentrations form this?

[Borek]

0.983 x H₂PO₄^- + H₂PO₄^- = 0.01

how am I to solve for the individual concentrations form this?

Looks to me like equation with one uknown. Simple algebra.

[Arkcon]

It is a little daunting at first.  What you've done is determined relative concentrations of the two buffer components -- the acid and base.  To actually make the buffer, you have to determine what volume and final concentration to apply the ratio to.

I have to admit 'tho, I'm glad Borek: conformed your calculations, because I would have used a different formula.

[student8607]

Oh. My brain was just fried  after trying to figure this buffer concept out I guess.
I get 0.00509 for H₂PO₄^-

so then 0.00500 for HPO₄^2-

STEP #3: MiVi=MfVf

0.00509M x 100mL = 0.1M x ?mL --> 5.09mL of H₂PO₄^-
0.00500M x 100mL = 0.1M x ?mL --> 5.00mL of HPO₄^2-

Does that look correct?

[Borek]

I have not checked the numbers thoroughly, I can just confirm that they look reasonable - pKa2 for phopsphoric acid is around 7.2 so to prepare pH=7.2 buffer you need almost identical amounts of acid and conjugate base, 5.00 vs 5.09 is just that - almost identical.

[AWK]

Oh. My brain was just fried  after trying to figure this buffer concept out I guess.
I get 0.00509 for H₂PO₄^-

so then 0.00500 for HPO₄^2-

STEP #3: MiVi=MfVf

0.00509M x 100mL = 0.1M x ?mL --> 5.09mL of H₂PO₄^-
0.00500M x 100mL = 0.1M x ?mL --> 5.00mL of HPO₄^2-

Does that look correct?

From a formal point of view your calculations are incorrect, since sum of both concentrations should be exactly 0.01! So concentrations should be 0.0504 and 0.0496 M

[student8607]

Can you pinpoint where I might have made a mistake?

The steps I got right out of our lab manual?

[AWK]

0.983 x H2PO4- + H2PO4- = 0.01

I calclulated these number from this eqation

[student8607]

0.983 x H2PO4- + H2PO4- = 0.01

How?

0.01/0.983 = 0.0107

then you have x + x = 0.0107
divide by two?
0.00509

[sjb]

0.983 x H2PO4- + H2PO4- = 0.01

How?

0.01/0.983 = 0.0107

then you have x + x = 0.0107
divide by two?
0.00509

Not quite.

You have something of the form ax + x = b, how do you solve for x? Factorise; so x(a + 1) = b, and so x = ^b/_{(a + 1)}

[student8607]

Not quite.

You have something of the form ax + x = b, how do you solve for x? Factorise; so x(a + 1) = b, and so x = ^b/_{(a + 1)}

so
x = 0.01/(0.983+1)

I get 0.00504M for H₂PO₄^-
& HPO₄^2- is 0.00496.

I still seem to be 1 decimal off from AWK's answer?

[Borek]

It must have been a typo on his side.

[student8607]

Alrighty. Thanks everyone.