When `20ml` of mixture of `O_(2)` and `O_(3)` is heated the volume becomes `29ml` and disappears in alkaline pyragallol solution. What is the volume percent of `O_(2)` in the original mixture ? .

Options

A. `90%`
B. `10%`
C. `18%`
D. `2%`

Explanation

To solve the problem step by step, we will follow these logical steps:

### Step 1: Understand the Mixture
We have a mixture of oxygen (O₂) and ozone (O₃) with a total volume of 20 ml. Let's denote the volume of ozone as \( x \) ml. Consequently, the volume of oxygen will be \( 20 - x \) ml.

### Step 2: Heating the Mixture
When the mixture is heated, ozone decomposes into oxygen:
\[ 2 \text{O}_3 \rightarrow 3 \text{O}_2 \]
This means that for every 2 volumes of ozone, 3 volumes of oxygen are produced.

### Step 3: Calculate the Volume of Oxygen Produced
From the volume of ozone \( x \):
- The volume of oxygen produced from \( x \) ml of ozone is:
\[ \text{Volume of O}_2 \text{ produced} = \frac{3}{2} x \text{ ml} \]

### Step 4: Total Volume After Heating
After heating, the total volume of gases becomes 29 ml. This total volume consists of:
- The original volume of oxygen \( (20 - x) \) ml
- The volume of oxygen produced from ozone \( \left(\frac{3}{2} x\right) \) ml

Thus, we can set up the equation:
\[ (20 - x) + \frac{3}{2} x = 29 \]

### Step 5: Solve the Equation
Now, we will solve the equation:
1. Combine the terms:
\[ 20 - x + \frac{3}{2} x = 29 \]
\[ 20 + \frac{1}{2} x = 29 \]
2. Isolate \( x \):
\[ \frac{1}{2} x = 29 - 20 \]
\[ \frac{1}{2} x = 9 \]
\[ x = 18 \text{ ml} \]

### Step 6: Determine the Volume of Oxygen
Now that we have \( x \):
- Volume of ozone \( = x = 18 \text{ ml} \)
- Volume of oxygen \( = 20 - x = 20 - 18 = 2 \text{ ml} \)

### Step 7: Calculate the Volume Percent of Oxygen
To find the volume percent of oxygen in the original mixture:
\[ \text{Volume percent of O}_2 = \left(\frac{\text{Volume of O}_2}{\text{Total Volume of Mixture}}\right) \times 100 \]
\[ \text{Volume percent of O}_2 = \left(\frac{2 \text{ ml}}{20 \text{ ml}}\right) \times 100 = 10\% \]

### Final Answer
The volume percent of \( O_2 \) in the original mixture is **10%**.

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