Question

use the $k_a$ values for weak acids to identify the best components for preparing buffer solutions with the given ph values.
name\tformula\t$k_a$
phosphoric acid\t$h_3po_4$\t$7.5\times10^{-3}$
acetic acid\t$ch_3cooh$\t$1.8\times10^{-5}$
formic acid\t$hcooh$\t$1.8\times10^{-4}$

ph = 3.9 choose...
ph = 1.9 choose...
ph = 5.0 choose...

Explanation:

Step1: Recall Henderson - Hasselbalch equation

For a buffer solution of a weak acid (HA) and its conjugate base ($A^-$), $pH = pK_a+\log\frac{[A^-]}{[HA]}$. The best - buffer is formed when $\log\frac{[A^-]}{[HA]} = 0$ (i.e., $[A^-]=[HA]$), so $pH\approx pK_a$. Calculate $pK_a=-\log K_a$ for each acid.

Step2: Calculate $pK_a$ for phosphoric acid

$pK_{a1}$ of $H_3PO_4$: $pK_{a1}=-\log(7.5\times 10^{-3})= 2.12$.

Step3: Calculate $pK_a$ for acetic acid

$pK_a$ of $CH_3COOH$: $pK_a = -\log(1.8\times 10^{-5})=4.74$.

Step4: Calculate $pK_a$ for formic acid

$pK_a$ of $HCOOH$: $pK_a=-\log(1.8\times 10^{-4}) = 3.74$.

Step5: Match $pK_a$ with given pH values

For $pH = 3.9$, the closest $pK_a$ is that of formic acid ($pK_a = 3.74$). For $pH = 1.9$, the closest $pK_a$ is that of phosphoric acid ($pK_{a1}=2.12$). For $pH = 5.0$, the closest $pK_a$ is that of acetic acid ($pK_a = 4.74$).

Answer:

$pH = 3.9$: formic acid ($HCOOH$)
$pH = 1.9$: phosphoric acid ($H_3PO_4$)
$pH = 5.0$: acetic acid ($CH_3COOH$)