Ionic product of water at $310 \,K$ is $2.7 \times 10^{-14}$. What is the $\mathrm{pH}$ of neutral water at this temperature?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Ionic product,  $K_{w}=\left[ H ^{+}\right]\left[ OH ^{-}\right]$

Let $\left[ H ^{+}\right]=x$

Since $\left[ H ^{+}\right]=\left[ OH ^{-}\right], K_{ w }=x^{2}$

$\Rightarrow K_{ w }$ at $310 \,K$ is $2.7 \times 10^{-14}$.

$\therefore 2.7 \times 10^{-14}=x^{2}$

$\Rightarrow x=1.64 \times 10^{-7}$

$\Rightarrow\left[ H ^{+}\right]=1.64 \times 10^{-7}$

$\Rightarrow pH =-\log \left[ H ^{+}\right]$

$=-\log \left[1.64 \times 10^{-7}\right]$

$=6.78$

Hence, the $pH$ of neutral water is $6.78$

Similar Questions

For a weak acid $HA,$ Ostwald's dilution law is represented by the equation

In aqueous solution the ionization constants for carbonic acid are

$K_1 = 4.2 \times 10^{-7}$ and $K_2 = 4.8 \times 10^{-11}$

Select the correct statement for a saturated $0.034\, M$ solution of the carbonic acid.

  • [AIEEE 2010]

When $100 \ mL$ of $1.0 \ M \ HCl$ was mixed with $100 \ mL$ of $1.0 \ M \ NaOH$ in an insulated beaker at constant pressure, a temperature increase of $5.7^{\circ} C$ was measured for the beaker and its contents (Expt. $1$). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $\left(-57.0 \ kJ \ mol ^{-1}\right)$, this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. $2$), $100 \ mL$ of $2.0 \ M$ acetic acid $\left(K_a=2.0 \times 10^{-5}\right)$ was mixed with $100 \ mL$ of $1.0 M \ NaOH$ (under identical conditions to Expt. $1$) where a temperature rise of $5.6^{\circ} C$ was measured.

(Consider heat capacity of all solutions as $4.2 J g ^{-1} K ^{-1}$ and density of all solutions as $1.0 \ g mL ^{-1}$ )

$1.$ Enthalpy of dissociation (in $kJ mol ^{-1}$ ) of acetic acid obtained from the Expt. $2$ is

$(A)$ $1.0$ $(B)$ $10.0$ $(C)$ $24.5$ $(D)$ $51.4$

$2.$ The $pH$ of the solution after Expt. $2$ is

$(A)$ $2.8$ $(B)$ $4.7$ $(C)$ $5.0$ $(D)$ $7.0$

Give the answer question $1$ and $2.$

  • [IIT 2015]

For a weak acid $HA$ with dissociation constant ${10^{ - 9}},\,\,pOH$ of its $0.1 \,M$  solution is

  • [AIPMT 1989]

Which among the given acids has lowest $pKa$ value