A given volume of a buffer solution contains $6.85 x 10^{- 3}$ $6.85 x 10^-3$ mol of the weak acid HY and $2.98 x 10^{- 3}$ $2.98 x 10^-3$ mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of $p K a$ $pKa$ for the acid HY at this temperature?

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A given volume of a buffer solution contains $6.85 x 10^{- 3}$ $6.85 x 10^-3$ mol of the weak acid HY and $2.98 x 10^{- 3}$ $2.98 x 10^-3$ mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of $p K a$ $pKa$ for the acid HY at this temperature?

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Answer 1 · 2018-06-27T16:53:00

Well, the buffer equation holds that.... $p H = p K_{a} + {log}_{10} {\frac{[Y^{-}]}{[H Y]}}$ $pH=pK_a+log_10{[[Y^-]]/[[HY]]}$ ...

...we finally get $pK_a=3.42...$

Explanation:

Now we were quoted molar quantities of the acid and its conjugate base....NOT concentrations...but given we have the quotient... $"concentration"="moles of solute"/"volume of solution"$ ...and in the buffer expression we get....

$log_10{((2.98.xx10^-3*mol)/(cancel"some volume"))/((6.85xx10^-3*mol)/cancel("some volume"))}$ ...that is the volumes cancel out....so WE DO NOT NEED TO KNOW THE VOLUME....

And so we solve for $pK_a$ in the buffer equation....

$pK_a=pH-log_10{(2.98xx10^-3*mol)/(6.85xx10^-3*mol)}$

$=3.78-underbrace(log_10{(2.98)/(6.85)})_"-0.361"=3.42$

$pH_"solution"$ is more acidic than $pK_a$ given that the parent acid is present in GREATER concentration.....to what would $pH$ be equal if $[HY]-=[Y^-]$ ?

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A given volume of a buffer solution contains $6.85 x 10^{- 3}$ $6.85 x 10^-3$ mol of the weak acid HY and $2.98 x 10^{- 3}$ $2.98 x 10^-3$ mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of $p K a$ $pKa$ for the acid HY at this temperature?

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Explanation:

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A given volume of a buffer solution contains 6.85 x 10^-36.85x10−36.85 x 10^-3 mol of the weak acid HY and 2.98 x 10^-32.98x10−32.98 x 10^-3 mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of pKapKapKa for the acid HY at this temperature?

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A given volume of a buffer solution contains $6.85 x 10^{- 3}$ $6.85 x 10^-3$ mol of the weak acid HY and $2.98 x 10^{- 3}$ $2.98 x 10^-3$ mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of $p K a$ $pKa$ for the acid HY at this temperature?