MCQ
The unit of ionic product of water ${K_w}$ are
  • A
    $Mo{l^{ - 1}}\,{L^{ - 1}}$
  • B
    $Mo{l^{ - 2}}\,{L^{ - 2}}$
  • C
    $Mo{l^{ - 2}}\,{L^{ - 1}}$
  • $Mo{l^2}\,{L^{ - 2}}$

Answer

Correct option: D.
$Mo{l^2}\,{L^{ - 2}}$
d
Ionic Product of water:

$\left. H _2 O ( l )+ H _2 O ( l ) \rightleftharpoons H _3 O ^{+} \text {(aq. }\right)+ OH ^{-} \text {(aq.) or }$

$H _2 O ( l ) \rightleftharpoons H _3 O ^{+}( aq )+ OH ^{-}( aq ) .$

As per laws of mass action : $K _{ c }=\frac{\left[ H ^{+}\right]\left[ OH ^{-}\right]}{\left[ H _2 O \right]}$

$K _{ c } \times\left[ H _2 O \right]= K _{ w }=\left[ H ^{+}\right]\left[ OH ^{-}\right]$

We can see that units of $K _w$ are equal to units of $\left[ H ^{+}\right] \times\left[ OH ^{-}\right]$

Units of $\left[ H ^{+}\right]=\left[ OH ^{-}\right]= mol \,L^{-1}$

$\therefore K _{ w }=\left( mol\, L ^{-1}\right)^2= mol ^2\, L ^{-2}$

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