What is the pH of a 1M HCN solution , $Ka=10^{-10}$ ?

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Answer 1 · 2018-07-11T11:48:41

$pH=5$

HCN $rightleftharpoons$ $H^+$ + $CN^-$
$K_a$ = [ $H^+$ ] [ $CN^-$ ] $//[HCN]$ = $10^-10$

HCN
$Initial_(HCN)=1M$
$Delta_(HCN)=-xM$
$Equilibrium_(HCN)=(1-x)M$

$H^+$
$Initial_(H^+)=0M$
$Delta_(H^+)=+xM$
$Equilibrium_(H^+)=xM$

$CN^-$
$Initial_(CN^-)=0M$
$Delta_(CN^-)=+xM$
$Equilibrium_(CN^-)=xM$

$K_a$ = [ $x$ ] [ $x$ ] $//[1-x]$ = $10^-10$ **
$=x^2 //1 =10^-10$
Here the x value can be ignored, and therefore x becomes 0 in $[1-x]$

$x=sqrt(10^-10)M$

$pH = -logx$
$pH = -logsqrt(10^-10)$
$pH=5$

What is the pH of a 1M HCN solution , Ka=10^{-10}Ka=10^{-10}?