Question

calculate the\[pH\], \[pOH\] and \[\left[ {{H^ + }} \right]ion\] concentration of
\[0.015{\text{ }}m{\text{ }}HCl\].

Answer 1

Hint: [pH\] is defined as the negative logarithm of \[{H^ + }\;ion\] concentration, Hence the meaning of the name \[pH\] is justified as the power of hydrogen as a\[pH{\text{ }} = {\text{ }} - log{\text{ }}\left[ {{H^ + }} \right]\] . The concentration of the hydroxide ion can be expressed logarithmically by the \[pOH\] . The \[pOH\] of a solution is the negative logarithm of the hydroxide-ion concentration and represent as a \[pOH{\text{ }} = {\text{ }} - log\left[ {OH{\;^{-\;}}} \right].\]

Complete Step by step answer: Assuming that this is done under standard conditions
Hydrochloric acid is a strong acid, it dissociates into single \[H + \;ions\] in an aqueous solution, which eventually become \[{H_3}O + \;ions\] due to the presence of water \[\left( {{H_2}O} \right).\]
In this problem, We can assume that\[\;HCl\;\] is completely ionized in water \[pH\] is given by the equation,
 \[pH = - log{\text{ }}\left[ {{H^ + }} \right]\]
\[\left[ {{H^ + }} \right]\;\] is the hydrogen ion concentration in terms of Molarity.
\[\;\left[ {{H^ + }} \right]\; = {\text{ }}0.015{\text{ }}m\; = {\text{ }}\left( {1.5{\text{ }} \times {{10}^{ - 2}}} \right)\]
Putting values of \[\left[ {H + } \right]\;\]
\[pH = - log{\text{ }}\left[ {{H^ + }} \right]\]
\[\Rightarrow pH = {\text{ }} - log{\text{ }}\left[ {1.5 \times {{10}^{ - 2}}} \right]\]
\[\Rightarrow pH = {\text{ }}2 - {\text{ }}log\frac{3}{2}\]
 \[\Rightarrow pH = {\text{ }}2 + log{\text{ }}2-log{\text{ }}3\] \[\therefore log3 = {\text{ }}0.477,log2 = 0.3010\]
\[\Rightarrow pH = 2 + {\text{ }}0.30-0.477\]
\[\Rightarrow pH = \;2.3 - 0.48\]
\[\Rightarrow pH\; = 1.88\]
we can use the following relationship -
\[pH\; + {\text{ }}pOH\; = 14{\text{ }}at{\text{ }}{25^ \circ }Celcius\]
\[1.88{\text{ }} + pOH{\text{ }} = 14\]
\[pOH\; = 12.12\]
Now the value of \[pH\], \[pOH\] and \[\left[ {{H^ + }} \right]ion\] concentration of \[0.015{\text{ }}m{\text{ }}HCl\] are
\[pH\] \[ = \;\;1.88\]
\[pOH\] \[ = \;\;12.12\]
\[\left[ {{H^ + }} \right]ion\]\[ = {\text{ }}1.5{\text{ }} \times {10^{ - 2}}\]


Note: The \[pH\] of a solution varies from\[0{\text{ }}to{\text{ }}14\] . Solutions having a value of pH ranging \[0{\text{ }}to{\text{ }}7\]on\[\;pH\] scale are termed as acidic and for the value of \[pH\] ranging \[7{\text{ }}to{\text{ }}14\] on \[pH\]scale are known as basic solutions when \[pH\] equal to \[7\] on \[pH\]scale are known as neutral solutions. Solutions having the value of \[pH\] equal to \[0\] are known to be strongly acidic solutions and solutions with the value of \[pH\] equal to \[14\] are termed as strongly basic solutions.