Question

Calculate the number of oxalic acid molecules in $100mL$ of $0.02N$ oxalic acid solution.

Answer 1

Hint: Think about the definition of what one mole of a substance is defined as. From this you will get an idea about how to convert the given concentration to the number of molecules present in a certain volume of the solution.

Complete step by step solution:
We know that the number of molecules present in one mole of any substance are $6.022\times {{10}^{23}}$ and is defined as the Avogadro’s number. So, to calculate the answer to this question, we will first need to calculate the number of moles of oxalic acid present in the given solution. For this, we will require the formula of normality and molarity.
The formulae for both these quantities are:
$N=M\times n$ for normality and
$M=\dfrac{m}{V}$ for molarity
Where, $N$ is the normality of the solution, $M$ is the molarity of the solution, $n$ is the n-factor or the basicity of the molecule, $m$ is the number of moles of solute, and $V$ is the volume of the solvent. Now we will take the equation for molarity and put it in the equation for normality and try to analyze if all the values are given to us. So the equation will be:
\[N=\dfrac{m\times n}{V}\]
The normality of the solution has been given to us as $0.02N$ and the volume of the solution has been given as $100mL=0.1L$, now we have to find the basicity of the molecule and then we will be able to find the number of moles. The basicity of an oxalic acid molecule is 2. This is because the formula of oxalic acid is ${{H}_{2}}{{C}_{2}}{{O}_{4}}$ where two of the hydrogens are acidic in nature and so, one mole of oxalic acid will be able to neutralize 2 moles of $O{{H}^{-}}$ ions. Now putting these values in the equation, we will solve for $m$.
\[\begin{align}
& N=\dfrac{m\times n}{V} \\
& 0.02=\dfrac{m\times 2}{0.1} \\
& m=\dfrac{0.002}{2} \\
& m=0.001moles \\
& m={{10}^{-3}}mol \\
\end{align}\]
Now, we will multiply the number of moles of oxalic acid present in the solution by Avogadro's number to obtain the number of molecules present.
\[\begin{align}
& \text{Number of molecules present}={{10}^{-3}}\times 6.022\times {{10}^{23}} \\
& \text{Number of molecules present}=6.022\times {{10}^{20}} \\
\end{align}\]

Note: Remember that the basicity of a substance does not indicate how basic a molecule is but the amount of base it will be able to neutralize. So, if a molecule has 1 acidic proton it will be able to neutralize 1 mole of hydroxyl ions and its basicity is 1. Similarly, a molecule with 3 acidic protons will have basicity 3.