Question

Acetyl salicylic acid $(mol.\;wt.\; = 180)$ called aspirin is a pain killer with $pKa\, = 6$. It two tablets each of $0.09\;gm$ mass containing aspirin are dissolved in $100\;mL\;$ solution. Its $pH$ will be:

A.$0.5$
B.$1.0$
C.$4.0$
D.$2.0$

Answer 1

$pH$ is a scale used to determine the acidity or basicity of an aqueous solution. It indicates the concentration of ${H^ + }$ or $O{H^ - }$ ions in the solution. In acidic and basic solutions, the concentration of hydrogen ions and hydroxide ions depends on the molarity of the solution. It is given as pH = - log{{ }}\left[ \text{concentration of H^+} \right]
The formula used: $pH\, = \dfrac{1}{2}\left[ {pKa - \log C} \right]$ where, $pKa$ is the negative log of the acid dissociation constant. The lower the value of $pKa$ the more acid will dissociate into ions in water.
So, to solve this we need to calculate the number of moles (concentration) and then calculate the $pH$ using the given $pKa$ value and concentration of acetylsalicylic acid.

Complete step by step answer:
Given, $pKa\, = 6$ and $mass = 0.09\;gm$
-Now we will calculate the total no. of moles in two tablets of Acetylsalicylic acid,
$No.\,of\,moles = \dfrac{{given\,mass}}{{molar\,mass}}$
$No.\,of\,moles = \dfrac{{2 \times 0.09}}{{180}} = 0.001$
$M = \dfrac{{no.\,of\,moles}}{{volume\,(\,l)}} = \dfrac{{0.001 \times 1000}}{{100}} = 0.01$ $(where\,M = molarity)$
-Now, the $pH$ will be; $pH\, = \dfrac{1}{2}\left[ {pKa - \log C} \right]$
$pH\, = \dfrac{1}{2}\left[ {6 - \log 0.01} \right] = \dfrac{1}{2}\left[ {6 - \left( { - 2} \right)} \right] = 4$
-Hence, the $pH$ of the Acetyl salicylic acid will be $4.0$
Therefore, Option (C) is correct.

Note:
Acetylsalicylic acid is a monoprotic acid. Monoprotic acids are weak acids which means that they can only donate one lone pair of electrons. This $pKa$ is defined as the value at which a chemical species accepts or donates a proton. The lower the $pKa$ value, the stronger will be the acid and greater will be its strength to donate a proton in aqueous solution. Acetylsalicylic acid has a variety of uses like relieving pain and swelling, conditions like flu, headache etcetera, and reducing the risk of cardiovascular diseases in people that have a high risk. There are some particular inflammatory conditions in which aspirin is used for treatment as Kawasaki disease, pericarditis, and rheumatic fever. The only thing that needs to be taken care of is its dose while using aspirin.