Question

Calculate pH of a solution whose \[100\;ml\]contains \[0.2g\;NaOH\] dissolved in it?
A. \[10.699\]
B. \[11.699\]
C. \[12.699\]
D. \[13.699\]

Answer 1

Hint:
The pH is equal to negative logarithm to the base ten of x, where, x is the hydrogen ion concentration unit is in moles per litre/s. When solute is base which is dissolved in neutral solvent here it is water, then the value of pH should be greater than seven as the base has a value greater than seven. The question here is what is the exact value of pH, for that the equation of pH is used.

Complete step by step solution
The range of pH scale is in between \[0\] to \[14\] including \[0\]and \[14\].The pH value is divided in three parts first, from \[0\] to \[7\] indicates the acidic nature of solution. Second, from \[7\] to \[14\] indicates the basic nature of the solution.

The intermediate value that is \[7\] indicates neutral nature of solution such as pure water or neutral substance which will not give hydrogen ion nor hydroxyl ion. The pH value of Ammonia or Sodium Hydroxide is in the range \[7\]-\[14\], which reflects their basic nature.

Whereas acidic substances like vinegar \[C{H_3}COOH\], stomach acid (\[HCl\]), battery acid, etc, show pH range from \[0\]-\[7\] is shown by acidic substances like vinegar \[C{H_3}COOH\], stomach acid (\[HCl\]), battery acid, etc, as per its acidic nature.

The concentration is expressed as follows:
\[Concentration{\rm{ }}\left( {Molarity} \right) = \dfrac{{moles{\rm{\; }}of{\rm{\; }}solute}}{{Volume{\rm{\; }}of{\rm{\; }}solution{\rm{ }}\left( {in{\rm{ \;}}litres} \right)}}\]
\[
Moles{\rm{ \;}}of{\rm{\; }}solute = {\rm{ \;}}\dfrac{{mass\;of\;sodium \;hydroxide}}{{molecular\;\;\;mass}}\\
 = \dfrac{{0.2}}{{40}}{\rm{ }}\\
 = {\rm{ }}0.005\;mol
\]

Volume of solution\[ = 100ml = \,0.1\,litres\].
\[
\left[ {OH - } \right] = \dfrac{n}{{volume}}\\
 = \dfrac{{0.005}}{{0.1}}\\
 = 0.05M
\]

\[
{pOH = - lo{g_{10}}\;\left[ {OH - } \right] = - lo{g_{10}}\left( {0.05} \right)\;}\\
{pOH{\rm{ }} = {\rm{ }}1.301}\\
{pH{\rm{ }} + {\rm{ }}pOH{\rm{ }} = {\rm{ }}14}\\
{Hence,{\rm{ }}pH{\rm{ }} = {\rm{ }}12.699}
\]

Therefore, the correct answer is option (C) \[12.699\].

Note:
In a few experiments the pH meter is used which indicates the exact value of pH same as a thermometer is used to measure the value of temperature, and a galvanometer is used for current.