Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: xshadow on February 04, 2016, 12:40:41 PM
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Hi!!
I have some doubt about the calculation of pH using the correct formula...
For example per the calculation ot the pH of a mixture of 2 weak acid i have the general formula:
[H+]= [A-]' + [A-]'' +[OH-]
' = acid 1
''= acid 2
Where:
[A-]' = k_a'/(k_a'+[H+]) * C'
[A-]'' = k_a''/(k_a''+[H+]) * C''
[OH-]= K_w/[H+]
[H+]= k_a'/(k_a'+[H+]) * C' + k_a''/(k_a''+[H+]) * C'' + K_w/[H+]
This is the General expression for the pH...but usually i need to do some semplification...
For example:
[H+] >> [OH-] i have:
[H+]= k_a'/(k_a'+[H+]) * C' + k_a''/(k_a''+[H+]) * C''
And this is only the first possible approximation...I could do others.
1) BUT the problem is: how can i verify if the approximation i used is correct?? C
2) What does it mean the" >> " from a numerical point of view in these expressions:
[H+] >> [OH-]
K_a' >> K_a''
How much the two terms must be different from a numerical point of view?? At lesson they said to us 10^2 or more? is correct?
3) and if I find:
pH>pk_a
pk_a' > pk_a''
How much must be the difference?? 1 or 2 unit?? or less? (0,...)
THANKS very much :)
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How much the two terms must be different from a numerical point of view?? At lesson they said to us 10^2 or more? is correct?
10^2 gives you erron of 5 % in concentration and ~0.02 pH unit
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How much the two terms must be different from a numerical point of view?? At lesson they said to us 10^2 or more? is correct?
10^2 gives you erron of 5 % in concentration and ~0.02 pH unit
Ok thanks :)
So if i have a condition like this:
pH > pKa ....in this case how much the difference must be to have an error of 5 % ??
If 10^2 (ka>>H+) gives me an error of 5 % in concentration and an error of 2% in pH unit to have an error of 5 % in pH unit (where H+ becomes pH and ka becomes pka so i get the expression pH>pka ) i have to do:
log_10 (0,005) = -1,3....so the difference must be 1,3 or more in order to use that approximated formula correctly ??
Thanks a lot.
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My comments concerned to an approximated formula
[H+] = SQRT(Ka1·c1 + Ka2·c2 + ... +Kw)
and pH ≈ -log([H+])
These approximations are valid in most calculations when ionic strength ≤ 0.01
When Ka1·c1 is at least 20 times higher then other parts of expression within square root.
1/20 =0.05 then [H+]=SQRT(c·1.05) ≈ 1.025·SQRT(c)
and -log(1.025)≈1.011
Last part Kw under square root is needed as correction when pH calculated without Kw is greater than 6.8
Examples:
0.1 M acetic acid and 0.5 M formic acid - may be treated as pure formic acid
0.005 M acetic acid and 0.001 M formic acid - both acids should be taken into account in calculations
5·10-10 M acetic acid and 1.0·10-10 M formic acid - addition of Kw is needed under square root
Check my examples by calculations!
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My comments concerned to an approximated formula
[H+] = SQRT(Ka1·c1 + Ka2·c2 + ... +Kw)
and pH ≈ -log([H+])
These approximations are valid in most calculations when ionic strength ≤ 0.01
When Ka1·c1 is at least 20 times higher then other parts of expression within square root.
1/20 =0.05 then [H+]=SQRT(c·1.05) ≈ 1.025·SQRT(c)
and -log(1.025)≈1.011
Last part Kw under square root is needed as correction when pH calculated without Kw is greater than 6.8
Examples:
0.1 M acetic acid and 0.5 M formic acid - may be treated as pure formic acid
0.005 M acetic acid and 0.001 M formic acid - both acids should be taken into account in calculations
5·10-10 M acetic acid and 1.0·10-10 M formic acid - addition of Kw is needed under square root
Check my examples by calculations!
So Ka1·C1 at least 20 times(for a 0,05 error) bigger than Ka2·C2 is equal to say that:
Ka1·C1 >> Ka2·C2
where >> is at least 102 (this "gap" give me in fact an error of 0,05)
Is it correct??
Thanks :)
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102 gives you error less than 1% for concentration and for pH less than 0,005 unit when ionic strength is negligible.
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But why before you said:
"10^2 gives you erron of 5 % in concentration and ~0.02 pH unit"??
Usually don't 10^2 give a concentration error of 5%?
Thanks.
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Students better remember 100 then 20. Moreover using 100 their results will be sufficiently correct (within 5 %) even with 1 significant digit.
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Students better remember 100 then 20. Moreover using 100 their results will be sufficiently correct (within 5 %) even with 1 significant digit.
IF I have understood correctly for an error of 5% is enough a difference of 20 times,right??
Thanks very much!
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Yes, 20 is sufficient for 5% error in concnetration of H+.
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Yes, 20 is sufficient for 5% error in concnetration of H+.
Thanks very MUCH :)