Hi, the question has some missing part. The complete question should be " If the [tex]pK_{a}[/tex] of [tex]HCHO_{2}[/tex] is 3.74 and the pH of an [tex]HCHO_{2}/NaCHO_{2}[/tex] solution is 3.89, it means that -
(a) [tex][HCHO_{2}]=[NaCHO_{2}][/tex]
(b) [tex][HCHO_{2}]> [NaCHO_{2}][/tex]
(c) [tex][HCHO_{2}]< [NaCHO_{2}][/tex]
Which of the options are true?"
Answer: Option (c) is true.
Explanation:
[tex]HCHO_{2}/NaCHO_{2}[/tex] is an weak acid-conjugate base buffer. Hence, in accordance with Henderson-Hasselbalch equation-
[tex]pH=pK_{a}(HCHO_{2})+log(\frac{[CHO_{2}^{-}]}{[HCHO_{2}]})[/tex]
Here, pH = 3.89, [tex]pK_{a}[/tex] of [tex]HCHO_{2}[/tex] = 3.74
So, [tex]3.89=3.74+log(\frac{[CHO_{2}^{-}]}{[HCHO_{2}]})[/tex]
or, [tex]\frac{[CHO_{2}^{-}]}{[HCHO_{2}]}[/tex] = 1.41 (>1)
So, [tex][CHO_{2}^{-}]> [HCHO_{2}][/tex]
or, [tex][NaCHO_{2}]> [HCHO_{2}][/tex]
Hence, option (c) is correct.
