b
\(\because\) Diliute solution given:

\(\frac{ P ^{0}- P _{ s }}{ P ^{0}} \sim \frac{{ }^{n} \text { solute }}{{ }^{n} \text { solvent }}\)

\(\frac{ P ^{0}- P ^{0} / 2}{ P ^{0}}=\frac{{ }^{n} \text { solute }}{ n _{\text {solvent }}}\)

" solute \(\sim \frac{{ }^{ n } \text { solvent }}{2}=\frac{100}{18 \times 2}=2.78 mol\)

More accurate approach:

\(\frac{ P ^{0}- P _{ S }}{ P _{ S }}=\frac{{ }^{ n } \text { solute }}{{ }^{n} \text { solvent }}\)

\(\frac{ P ^{0}- P ^{0} / 2}{ P ^{0} / 2}=\frac{{ }^{n} \text { solute }}{{ }^{n} \text { solvent }}\)

\(\text { " solute }={ }^{n} \text { solvent }=\frac{100}{18}=5.55 mol\)