Question

Aspirin is a pain reliever with ${\text{p}}{{\text{K}}_{\text{a}}}$ ​= 2 . Two tablets each containing $0.09{\text{ g}}$ of aspirin-are dissolved in 100mL solution. pH will be:

A)0.5
B)1.0
C)0.8
D)2.0

Answer 1

To answer this question, you should recall the concept of calculation of pH. It is a quantitative measure of the acidity or basicity of a liquid solution. Calculate the concentration of hydrogen ions in the solution and use it to calculate the pH of the weak acid.

Formula used:
${\text{Molarity}} = \dfrac{{{\text{Weight of solute}} \times {\text{1000}}}}{{{\text{Molar mass of solute}} \times {\text{Vol}}{\text{. of solution(ml)}}}}$ --(i)
${\text{pH = }}\dfrac{1}{2}({\text{p}}{{\text{K}}_{\text{a}}} - {\text{logC}})$ ---(ii) where ${{\text{K}}_{\text{a}}}$is dissociation constant and ${\text{C}}$ is concentration or molarity of hydrogen ions in the solution.

Complete Step by step solution:
First talking about aspirin we know that aspirin, also known as acetylsalicylate belongs to the class of organic compounds known as acetylsalicylic acids. It is a derivative of salicylic acid is an orally administered non-steroidal anti-inflammatory agent. In the body acetylsalicylic acid binds to and acetylates serine residues in cyclooxygenases, resulting in decreased synthesis of prostaglandin, platelet aggregation, and inflammation.
To find the answer to this question let us first calculate the molarity of this solution. We are given two tablets hence the dissolved weight of solute is $2 \times 0.09 = 0.18{\text{ g}}$. The molar mass of aspirin is $180.15{\text{ g}}$. The volume of the solution is given as 100ml.
$\therefore$Molarity can be calculated using the formula in equation (i)
$\Rightarrow \dfrac{{2 \times 0.09 \times 1000}}{{180.15 \times 100}} = 0.01{\text{M}}$.
Now as aspirin is a weak acid. The pH of a weak acid is given by equation (ii). Thus the pH can be calculated as:
${\text{pH = }}\dfrac{1}{2}({\text{p}}{{\text{K}}_{\text{a}}} - {\text{logC}}) = \dfrac{1}{2}\left( {2 + 2} \right) = 2$
Hence, the correct answer is 2.0.
Therefore, we can conclude that the correct answer to this question is option D.

Note: You should remember the difference between strong acids and weak acids: a strong acid is $100\%$ionized in solution but if it is less than $100\%$ ionized in solution, it is a weak acid. There are very few strong acids and certain salts will also affect the acidity or basicity of aqueous solutions because some of the ions will undergo hydrolysis. The general rule is that salts with ions that are part of strong acids or bases will not hydrolyse, while salts with ions that are part of weak acids or bases will hydrolyse