Question

50 mL of $1M$ oxalic acid (molar mass of oxalic acid = 126) is shaken with 0.5g of wood charcoal. The final concentration of the solution after adsorption is $0.5M$. Calculate the amount of oxalic acid absorbed per gram of charcoal?

Answer 1

Hint: Try to recall that adsorption is the phenomenon of higher concentration of molecular species on the surface of solid than in the bulk. Also, the amount of acid absorbed is the final mass of oxalic acid minus initial mass. Now, by using this you can easily find the answer.

Complete step by step answer:
- We know that molarity is defined as the number of moles of solute in a given volume of solution. The formula for molarity is:
\[\text{molarity}=\dfrac{\text{number of moles}}{\text{volume}}\]

- The number of moles of any substance present can be calculated by dividing the given mass of the substance by the molecular mass. The formula is:
\[\text{number of moles}=\dfrac{\text{given weight}}{\text{molecular weight}}\]

- Calculation:
Let the amount of oxalic acid initially present be $w$
- Given information:
Initial concentration of solution, $M=1M$
Molar mass of oxalic acid, $m=126g/mol$
Initial volume of solution, $V=50mL=0.05L$
Initial moles of oxalic acid,
Using the formula for molarity, we can calculate the number of moles of oxalic acid present.
\[\begin{align}
  & \text{molarity}(M)=\frac{\text{number of moles}(n)}{\text{volume}(V)} \\
 & n=M\times V \\
 & n=1\times 0.05 \\
 & n=0.05 \\
\end{align}\]

So, using the formula for the number of moles, we can calculate the amount of oxalic acid present initially.
\[\begin{align}
  & \text{number of moles}(n)=\dfrac{\text{given weight}(w)}{\text{molecular weight}(m)} \\
 & w=n\times m \\
 & w=0.05\times 126 \\
 & w=6.3g \\
\end{align}\]

- After adsorption:
Concentration of solution, $M'=0.5M$
Volume of solution, $V=0.05L$
Using formula for molarity, we get:
\[\begin{align}
  & n'=M'\times V \\
 & n'=0.5\times 0.05 \\
 & n'=0.025 \\
\end{align}\]
Now, using the formula for the number of moles:
\[\begin{align}
  & w'=n'\times m \\
 & w'=0.025\times 126 \\
 & w'=3.15g \\
\end{align}\]

Now, to calculate the amount adsorbed, we will subtract the weight after adsorption from the weight before adsorption.
\[\begin{align}
 & \text{amount adsorbed}=6.3-3.15 \\
 & \text{amount adsorbed}=3.15g \\
\end{align}\]
Mass of wood charcoal on which adsorption takes place = 0.5g
Hence, amount of adsorbed per gram of charcoal will be:
\[\begin{align}
 & \text{amount adsorbed per gram of charcoal}=\dfrac{3.15}{0.5} \\
 & \text{amount adsorbed per gram of charcoal}=6.5g \\
\end{align}\]
Hence, we can say that the amount of substance adsorbed on the surface of one gram of charcoal is 6.5g.

Note: Note that the extent of adsorption of a gas on a solid tends to increase with decrease of temperature and increase of pressure. Also, you should remember that the extent of adsorption increases with increase in concentration of solute in solution.