# Question a39a6

Mar 21, 2016

Here's what I got.

#### Explanation:

The idea here is that concentrated sulfuric acid will act as a dehydrating agent and remove water molecules from the two acids.

Concentrated sulfuric acid will dehydrate formic acid, $\text{HCOOH}$, to produce water and carbon monoxide, $\text{CO}$, according to the balanced chemical equation

${\text{HCOOH"_text((l]) stackrel(color(red)("H"_2"SO"_text(4(l]))color(white)(aaa))(->) "H"_2"O"_text((l]) + "CO}}_{\textrm{\left(g\right]}}$ $\uparrow$

Notice that you have a $1 : 1$ mole ratio between formic acid and carbon monoxide. This means that if you take $x$ to be the number of moles of formic acid present in the mixture, you can say that the dehydration reaction will produce $x$ moles of carbon monoxide.

Sulfuric acid will dehydrate oxalic acid, ${\text{H"_2"C"_2"O}}_{4}$, to produce water and a mixture of carbon monoxide and carbon dioxide, ${\text{CO}}_{2}$, according to the balanced chemical equation

${\text{H"_2"C"_2"O"_text(4(l]) stackrel(color(red)("H"_2"SO"_text(4(l]))color(white)(aaa))(->) "H"_2"O"_text((l]) + "CO}}_{\textrm{\left(g\right]}}$ $\uparrow + {\text{CO}}_{\textrm{2 \left(g\right]}} \uparrow$

Once again, you have $1 : 1$ mole ratios between oxalic acid and the two gaseous products. This means that if you take $y$ to be the number of moles of oxalic acid in the mixture, you can say that the dehydration reaction will produce $y$ moles of carbon monoxide and $y$ moles of carbon dioxide.

Your goal here is to find the ratio that exists between the number of moles of formic acid and the number of moles of oxalic acid, ie.e $\frac{x}{y}$.

The total number of moles of gas produced by the dehydration reaction will be equal to

n_"total" = x + y + y = overbrace((x+y))^(color(purple)("moles of CO")) + overbrace(y)^(color(blue)("moles of CO"_2)) = x + 2y#

Now, the trick is to recognize the fact that potassium hydroxide, $\text{KOH}$, will only react with the carbon dioxide.

Since the gaseous mixture is kept under the same conditions for pressure and temperature, a decrease in volume is equivalent to a decrease in number of moles.

In other words, the volume of the mixture decreases because the moles of carbon dioxide are absorbed by the potassium hydroxide solution.

The mole fraction of carbon dioxide in the mixture will be equal to

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\chi}_{C {O}_{2}} = \text{number of moles of CO"_2/"total number of moles of gas}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

${\chi}_{C {O}_{2}} = \left(y \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))))/((x + 2y)color(red)(cancel(color(black)("moles}}}}\right) = \frac{y}{x + 2 y}$

If all the moles of carbon dioxide were absorbed by the solution, you can say that the mole fraction of carbon dioxide in the mixture is equivalent to

$\frac{y}{x + 2 y} = \frac{1}{6}$

This will be equivalent to

$6 y = x + 2 y$

$4 y = x \implies \frac{x}{y} = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{4}{1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The mixture contained four time more moles of formic acid than of oxalic acid.