Question

The $ \left[ {O{H^ - }} \right] $ in a solution is 1 $ {\text{mol }}{{\text{L}}^{ - 1}} $ . The pH of the solution is:
(A) 1
(B) 0
(C) 14
(D) $ {10^{ - 14}} $

Answer 1

Hint: pH is a scale used to specify whether a solution is acidic or basic. The scale of pH is logarithmic. The sum of pH and pOH is 14. pH can be calculated by the given formula.
 $ pH = - \log \left[ {{H^ + }} \right] $

Complete Step by step solution:
Acidic solutions have lower pH value and basic or alkaline solutions have higher pH values.
The pH scale indicates inversely the concentration of hydrogen ions in the solution. pOH of any solution is the negative logarithm of hydroxide ion concentration.
A basic solution has pOH less than 7 and pH more than 7 whereas an acidic solution has pH less than 7 and pOH more than 7. The less the value of pH more, $ {H^ + } $ ion concentration is present in the solution. Also, pH scale changes if there is a change in temperature.
pH + pOH = pKw
Kw is the equilibrium constant for the reaction called an ion product constant of liquid water.
Kw = $ \left[ {{H_3}{O^ + }} \right] $ $ \left[ {O{H^ - }} \right] $
At $ {25^ \circ } $ C, the value of pKw is 14.
At $ {25^ \circ } $ C, pH + pOH = 14
 $ pH = - \log \left[ {{H^ + }} \right] $ and $ pOH = - \log \left[ {O{H^ - }} \right] $
The $ \left[ {O{H^ - }} \right] $ indicates molarity of hydroxide ion which is one here.
 $ pOH = - \log \left[ 1 \right]\left[ 1 \right] $
The value of log 1 is zero.
Hence, $ pH + pOH = 14 $
 $ pH + 0 = 14 $
Therefore, pH = 14
Hence the pH of the solution is 14. The correct option is C.

Note:
pH + pOH = pKw is valid at all temperatures. But pKw =14 is valid only at $ {25^ \circ } $ C.
pH = pOH which is equal to 7 at $ {25^ \circ } $ C. The acids that are completely dissociated in water are called as strong acids and the bases that are completely dissociated in water are called as strong bases respectively.