Question

If $50{\text{ mL}}$of $1{\text{ M}}$ oxalic acid (molar mass$ = 126$) is shaken with $0.5{\text{ g}}$ of wood charcoal. The final concentration of the solution after adsorption is $0.5{\text{ M}}$. What is the amount of oxalic acid absorbed per gram of carbon?
$3.15$
$1.575$
$6.30$
$12.60$

Answer 1

Hint: In the question, the molarity of the oxalic acid solution before and after the adsorption on wood charcoal is given. Using the formula for molarity of the solution, since the volume is known, we can find the amount of oxalic acid adsorbed on the surface of charcoal. You must recall the formula used for calculating the molarity of a solution.
Formula used:
 The molarity of a solution is given by, ${\text{M}} = \dfrac{n}{V}$
Where, $M$ is the molarity of the given solution.
$n$ is the number of moles of the solute in the solution
And $V$ is the volume of the given solution, expressed in liters.

Complete step by step answer:
 We are given in the question, the volume of the oxalic acid solution as $V = 50{\text{ mL}}$ and the initial molarity as $1{\text{ M}}$. The mass of wood charcoal added is $0.5{\text{ g}}$.
Using the formula for molarity, we calculate the number of moles of oxalic acid present initially in the solution, as $M = \dfrac{{{n_i}}}{V}$
$ \Rightarrow {n_i} = 1{\text{M}} \times 0.05{\text{L}}$
$ \Rightarrow n = 0.05{\text{ mol}}$
The molarity of the solution after adsorption is given as $0.5{\text{ M}}$. So the number of moles of oxalic acid in the solution now becomes, ${n_f} = {M_f} \times V$
\[ \Rightarrow {n_f} = 0.5{\text{M}} \times 0.05{\text{L}}\]
$ \Rightarrow {n_f} = 0.025{\text{ moles}}$
So the number of moles of oxalic acid adsorbed by $0.5{\text{ g}}$ of the wood charcoal is $0.025$ moles.
So the oxalic acid adsorbed per gram of wood charcoal will be $\dfrac{{0.025}}{{0.5}} = 0.05$ moles
We know that the molar mass of oxalic acid is $126{\text{ g/mol}}$
Hence, the mass of oxalic acid adsorbed per gram of wood charcoal is
$m = n \times {M_o}$
Substituting the values:
$ \Rightarrow m = 0.05{\text{ mol}} \times {\text{126 g/mol}}$
$ \Rightarrow m = 6.30{\text{g}}$

Hence, the correct answer is C.

Note:
In molarity, the volume of solution is expressed in terms of liters. The volume in question is given in milliliters, so it is important to convert it into liters to obtain the correct answer. Molarity is dependent on the temperature as well.