Respuesta :
Answer : The mass of sodium acetate is, 1.097 grams.
Explanation : Given,
The dissociation constant for acetic acid = [tex]K_a=1.8\times 10^{-5}[/tex]
Concentration of acetic acid (weak acid)= 0.20 M
volume of solution = 125. mL
pH = 4.47
First we have to calculate the value of [tex]pK_a[/tex].
The expression used for the calculation of [tex]pK_a[/tex] is,
[tex]pK_a=-\log (K_a)[/tex]
Now put the value of [tex]K_a[/tex] in this expression, we get:
[tex]pK_a=-\log (1.8\times 10^{-5})[/tex]
[tex]pK_a=5-\log (1.8)[/tex]
[tex]pK_a=4.74[/tex]
Now we have to calculate the concentration of sodium acetate (conjugate base or salt).
Using Henderson Hesselbach equation :
[tex]pH=pK_a+\log \frac{[Salt]}{[Acid]}[/tex]
Now put all the given values in this expression, we get:
[tex]4.47=4.74+\log (\frac{[Salt]}{0.20})[/tex]
[tex][Salt]=0.107M[/tex]
Now we have to calculate the mass of sodium acetate.
[tex]\text{Concentration}=\frac{\text{Mass of }NaCH_3CO_2\times 1000}{\text{Molar mass of }NaCH_3CO_2\times \text{Volume of solution (in mL)}}[/tex]
[tex]0.107M=\frac{\text{Mass of }NaCH_3CO_2\times 1000}{82g/mol\times 125mL}[/tex]
[tex]\text{Mass of }NaCH_3CO_2=1.097g[/tex]
Therefore, the mass of sodium acetate is, 1.097 grams.
