Question

500ml of 0.02M acetic acid are added to 500ml of 0.03M sodium acetate solution. If the dissociation constant of acetic acid is $1.5\times {{10}^{-5}}$ then pH of resulting solution is:
A. 5.0
B. 9.0
C. 3.0
D. 4.0

Answer 1

Hint: pH or potential of hydrogen is a scale used to specify the acidity or basicity of an aqueous solution. Acetic acid is a weak acid and for weak acid, set up the equilibrium expression for dissociation to ions in solution, then solve this equation for the hydronium ion concentration.

Complete step by step solution:
Acetic acid is weak acid and sodium acetate is a salt of weak acid and strong base.
We are given with the concentration of acetic acid and of sodium acetate with ${{\text{K}}_{\text{a}}}\text{= 1}\text{.5 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-5}}}$also given.
We will use the formula $\text{pH = p}{{\text{K}}_{\text{a}}}\text{+log }\!\![\!\!\text{ }\dfrac{\text{C}{{\text{H}}_{\text{3}}}\text{COONa}}{\text{C}{{\text{H}}_{\text{3}}}\text{COOH}}\text{ }\!\!]\!\!\text{ }$.
Putting the value of all we get, $\text{pH = -(log 1}\text{.5 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-5}}}\text{) + log }\!\![\!\!\text{ }\dfrac{\text{0}\text{.3}}{\text{0}\text{.2}}\text{ }\!\!]\!\!\text{ }$.
After simplification the above we get, -log 1.5 +5 + log 1.5=5.
So, our final answer comes as 5.0 therefore, option A is correct.

Additional Information:
The range of pH goes from 0 to 14, with 7 being neutral.
pH less than 7 indicates acid, whereas a pH of greater than 7 indicates a base.
It is a measure of the relative amount of free hydrogen and hydroxyl ions in the water.

Note: Remember that amount of substance does not affect its pH but the concentration does. Apart from concentration, there are factors such as pressure and temperature on which the pH depends. If the pressure increases the pH decreases. In case of temperature if the temperature increases pH decreases.