Question

One mole of a mixture of $CO$ and $C{O_2}$ requires exactly $20gm$ of $NaOH$ in solution for complete conversion of all the $C{O_2}$ into $N{a_2}C{O_3}$. How many moles more of $NaOH$ would it require for conversion into $N{a_2}C{O_3}$ if the mixture (one mole) is completely oxidized to $C{O_2}$?
A) $0.2$
B) $0.5$
C) $0.4$
D) $1.5$

Answer 1

The required reaction is $2NaOH + C{O_2} \to N{a_2}C{O_3} + {H_2}O$. Get the initial number of moles of $C{O_2}$ present. From that we can deduce the number of moles of $CO$ also.

Complete answer:
Total moles of $CO$ and $C{O_2}$ is given that $1$.
So, let's say the number of moles of $CO$ is $x$. So, the number of moles of $C{O_2}$ will be $\left( {1 - x} \right)$
Now, let us look at the reaction between sodium hydroxide and carbon dioxide. The reaction will produce sodium carbonate as a product. The required reaction is:
$2NaOH + C{O_2} \to N{a_2}C{O_3} + {H_2}O$
So, from the above chemical equation, it is obvious that $2$ moles of $NaOH$ react with $1$ mole of $C{O_2}$.
Now, we are given $20gm$ of $NaOH$, which means $0.5$ moles of $NaOH$.
So, $0.5$ moles of $NaOH$ will react with $\dfrac{{0.5}}{2} = \dfrac{1}{4} = 0.25$ moles of $C{O_2}$.
So, we get the moles of $C{O_2}$ is $0.25$ moles.
So, the moles of $CO$ will be $x = \left( {1 - 0.25} \right) = 0.75$ moles.
Now, $1$ mole of $C{O_2}$ reacts with $2$ moles of $NaOH$.
So, $0.25$ moles of $C{O_2}$ react with $\left( {2 \times 0.25} \right) = 0.5$ moles of $NaOH$.
So, it would require $\left( {2 - 0.5} \right) = 1.5$ moles more of $NaOH$ for conversion into $N{a_2}C{O_3}$ if the mixture (one mole) is completely oxidized to $C{O_2}$.
Hence the correct answer is option C.

Note:
The concept of this question is based on the law of constant combination. It is also sometimes called the law of definite proportion. The law of definite proportions states that a chemical compound always consists of the same elements, combines together in the same proportion by mass and it does not depend on its source and method of preparation. It is also called the Proust’s law.