Explanation:

When a mixture of formic acid (HCOOH) and oxalic acid (H2C2O4) is heated with concentrated sulfuric acid (H2SO4), a gas is produced. This gas is collected and treated with potassium hydroxide (KOH) solution. As a result, the volume of the solution decreases by 1/6th.

To understand the molar ratio of the two acids in the original mixture, let's break down the reaction steps and analyze the changes that occur.

Step 1: Reaction with H2SO4
When the mixture of formic acid and oxalic acid is heated with concentrated sulfuric acid, an esterification reaction takes place. This reaction is known as Fischer esterification. The general equation for Fischer esterification is:

Carboxylic acid + Alcohol ⇌ Ester + Water

In this case, formic acid and oxalic acid act as carboxylic acids, and sulfuric acid acts as a catalyst. The esterification reaction can be represented as follows:

HCOOH + H2SO4 ⇌ HCOOSO3H + H2O

H2C2O4 + H2SO4 ⇌ HOOCOSO3H + H2O

Step 2: Reaction with KOH Solution
The gas produced from the esterification reaction is collected and treated with potassium hydroxide solution. This step involves the saponification reaction, which converts the ester back into the carboxylic acid and alcohol. The general equation for saponification is:

Ester + Base ⇌ Carboxylic acid + Alcohol

In this case, the ester formed in the esterification reaction is reacted with KOH solution:

HCOOSO3H + KOH ⇌ HCOOK + H2SO4

HOOCOSO3H + KOH ⇌ KOOCO2H + H2SO4

Volume Decrease
The volume of the solution decreases by 1/6th after the treatment with KOH solution. This decrease in volume indicates that one of the products of the saponification reaction is a gas. Since the gas is collected, it does not contribute to the decrease in volume. Therefore, the decrease in volume is due to the formation of sulfuric acid (H2SO4) as a byproduct of the saponification reaction.

Molar Ratio Calculation
To determine the molar ratio of the two acids in the original mixture, we need to consider the stoichiometry of the reactions. From the esterification reaction, we can see that for every one molecule of formic acid or oxalic acid, one molecule of sulfuric acid is consumed. Therefore, the molar ratio of the two acids in the original mixture is 1:1.

In conclusion, when a mixture of formic acid and oxalic acid is heated with concentrated sulfuric acid, an esterification reaction occurs. The gas produced is collected and treated with KOH solution, resulting in a decrease in volume due to the formation of sulfuric acid. The molar ratio of the two acids in the original mixture is 1:1.