Calculate the change in $\mathrm{pH}$ when a $0.1 M$ solution of $C{H}_{3}COOH$ in water at $25° \mathrm{C}$ is diluted to a final concentration of $0.01\mathrm{M}\cdot \left[K_a=1.85\times {10}^{-5}\right]$

${\mathrm{CH}}_{3}COOH\to \text{ Weak acid. }$

$ph=\frac{1}{2}(pka-\log z)$

$\text{ pH initial }=\frac{1}{2}\text{ Lpka- }\log c_{initial}$

${p^H}^{\prime }\text{ final}=\frac{1}{2}\left[p{x}_a-\log C_{\text{final }}\right]$

$\mathrm{\Delta }{p}^H=p^H\text{ final }-{P^H}_{initial}$

$=\frac{1}{2}\left[\log C_{\text{initial }}-\log C_{\text{final }}\right]$

$\mathrm{\Delta }{p}^H=\frac{1}{2}\left[\log \right(0.1)-\log (0.01\left)\right]$

$=\frac{1}{2}\left[\right(-1)-(-2\left)\right].$

$\mathrm{\Delta }ph=\frac{1}{2}[-1+2]=\frac{1}{2}$

$=0.5$