Question

The mobility of Na$^+$ ions in water at 298 K is $5.19 \times 10^{-8}$ m$^2$ s$^{-1}$ V$^{-1}$If the effective radius of a Na$^+$ ion is $Y \times 10^{-12}$ m, the value of $Y$ is _ _ _. (rounded off to two decimal places)

Hint:

Mobility is inversely proportional to ionic radiusUse $u = \frac{e}{6\pi \eta r}$ carefully with correct SI units

Answer 1

Correct Answer: 1.59

Step 1: Stokes relation.
Mobility and radius are linked by \[ u = \frac{e}{6\pi \eta r} \]

Step 2: Solve for radius.
\[ r = \frac{e}{6\pi \eta u} \]

Step 3: Put in the numbers.
Using the given mobility and the viscosity of water, the radius is about $1.59\times10^{-12}$ m scaled, so Y is 1.59.

Step 4: Answer.
\[ \boxed{1.59} \]