A mixture of formic acid and oxalic acid is heated with conc. `H_(2)SO_(4)`. The gas producted is collected and treated with `KOH` solution, whereby the volume decrease by `1//6th`. The molar ratio of the two acids (formic acid/oxalic acid) is

Options

A. `4:1`
B. `1:4`
C. `2:1`
D. `1:2`

Explanation

To solve the problem of finding the molar ratio of formic acid (HCOOH) to oxalic acid (H2C2O4) when heated with concentrated sulfuric acid (H2SO4), we can follow these steps:

### Step 1: Understand the Reactions
When formic acid and oxalic acid are heated with concentrated sulfuric acid, they decompose to produce gases. The reactions are as follows:

1. **For Formic Acid (HCOOH)**:
\[ \text{HCOOH} + \text{H}_2\text{SO}_4 \rightarrow \text{CO} + \text{H}_2\text{SO}_4 + \text{H}_2\text{O} \]
This reaction produces 1 mole of carbon monoxide (CO) for each mole of formic acid.

2. **For Oxalic Acid (H2C2O4)**:
\[ \text{H}_2\text{C}_2\text{O}_4 + \text{H}_2\text{SO}_4 \rightarrow \text{CO} + \text{CO}_2 + \text{H}_2\text{SO}_4 + \text{H}_2\text{O} \]
This reaction produces 1 mole of CO and 1 mole of carbon dioxide (CO2) for each mole of oxalic acid.

### Step 2: Define Moles of Acids
Let:
- \( x \) = moles of formic acid (HCOOH)
- \( y \) = moles of oxalic acid (H2C2O4)

### Step 3: Calculate Total Moles of Gas Produced
From the reactions:
- Moles of CO produced from formic acid = \( x \)
- Moles of CO produced from oxalic acid = \( y \)
- Moles of CO2 produced from oxalic acid = \( y \)

Total moles of gas produced:
\[ \text{Total moles} = x + y + y = x + 2y \]

### Step 4: Analyze the Volume Change with KOH
When the gas mixture is treated with KOH, CO2 is absorbed, leading to a decrease in volume by \( \frac{1}{6} \). This means that the volume of CO2 absorbed is \( \frac{1}{6} \) of the total volume of gas.

### Step 5: Set Up the Equation
The fraction of CO2 in the total gas is given by:
\[ \frac{y}{x + 2y} = \frac{1}{6} \]

### Step 6: Cross-Multiply and Solve for x and y
Cross-multiplying gives:
\[ 6y = x + 2y \]
Rearranging gives:
\[ 6y - 2y = x \implies 4y = x \]

### Step 7: Determine the Molar Ratio
The molar ratio of formic acid to oxalic acid is:
\[ \frac{x}{y} = \frac{4y}{y} = 4:1 \]

### Final Answer
The molar ratio of formic acid to oxalic acid is \( 4:1 \).

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