A `0.002 M` aqueous solution of an ionic compound `[Co(NH_(3))_(5)(NO_(2))] Cl` freezes at `-0.00732^(@)C`. Find the number of moles of ions which `1` mole of ionic compound produces of being dissolved in water. `(K_(f) = -1.86^(@)C//m)`.

Options

A. 2
B. 3
C. 4
D. 1

Answer

A

Explanation

Given, molality, m = 0.0020 m
`Delta T_(f)=0^(@)C-0.00732^(@)C=-0.00732^(@)C`
`K_(f)=-1.86^(@)C//m`
`Delta T_(f)=i.K_(f)xx m`
`i=(Delta T_(f))/(K_(f)xx m)=(0.00732)/(1.86xx0.0020)=1.96~~2`
Since, the compound is ionic, so number of moles produced is equal to van't Hoff factor, i.
Hence, 2 moles of ions are produced.
`[Counderset("1 mol")((NH_(3))_(5)NO_(2))]Cl rarr underset("2 ions")(underbrace([Co(NH_(3))_(5)NO_(2)]^(+)+Cl^(-)))`