The ratio of the gases obtained on dehydration of `HCOOH` and `H_2 C_2 O_4` by `conc .H_2SO_4` is

Options

A. `2 : 1`
B. `1 : 2`
C. `3 : 1`
D. `1 : 3`

Explanation

To solve the problem of finding the ratio of gases obtained on dehydration of formic acid (HCOOH) and oxalic acid (H₂C₂O₄) by concentrated sulfuric acid (H₂SO₄), we will follow these steps:

### Step 1: Understand the dehydration reaction of formic acid (HCOOH)
When formic acid is heated with concentrated sulfuric acid, it undergoes dehydration. The reaction can be represented as follows:

\[ \text{HCOOH} \xrightarrow{\text{conc. } H_2SO_4, \text{ heat}} \text{CO} + \text{H}_2O \]

In this reaction, formic acid produces carbon monoxide (CO) and water (H₂O). The gas released here is carbon monoxide.

### Step 2: Identify the number of gases produced from formic acid
From the reaction of formic acid, we see that only **one gas** is produced, which is carbon monoxide (CO).

### Step 3: Understand the dehydration reaction of oxalic acid (H₂C₂O₄)
Next, we consider the dehydration of oxalic acid. The reaction can be represented as follows:

\[ \text{H}_2\text{C}_2\text{O}_4 \xrightarrow{\text{conc. } H_2SO_4, \text{ heat}} \text{CO} + \text{CO}_2 + \text{H}_2O \]

In this reaction, oxalic acid produces both carbon monoxide (CO) and carbon dioxide (CO₂) along with water (H₂O).

### Step 4: Identify the number of gases produced from oxalic acid
From the reaction of oxalic acid, we see that **two gases** are produced: carbon monoxide (CO) and carbon dioxide (CO₂).

### Step 5: Calculate the ratio of gases produced
Now, we can calculate the ratio of gases produced from the dehydration of formic acid to that of oxalic acid:

- Gases from formic acid: 1 (CO)
- Gases from oxalic acid: 2 (CO and CO₂)

Thus, the ratio of gases is:

\[ \text{Ratio} = \frac{\text{Number of gases from formic acid}}{\text{Number of gases from oxalic acid}} = \frac{1}{2} \]

### Conclusion
The required ratio of the gases obtained on dehydration of formic acid and oxalic acid by concentrated sulfuric acid is **1:2**.