A mixture of 15 ml of CO & `CO_2` is mixed with V ml (excess) of oxygen and electrically sparked. The volume after explosion was found to be (V+12) ml. What would be the residual volume if 25 ml of the original mixture is exposed to an alkali?

Options

A. 7ml
B. 12ml
C. 10ml
D. 9ml

Answer

To solve the problem step by step, let's break it down systematically.

### Step 1: Understand the Reaction
We have a mixture of carbon monoxide (CO) and carbon dioxide (CO₂) that reacts with excess oxygen (O₂) when electrically sparked. The reaction can be summarized as follows:

- **Reaction of CO with O₂:**
\[ 2 \text{CO} + \text{O}_2 \rightarrow 2 \text{CO}_2 \]

### Step 2: Write Down Given Data
From the problem, we have:
- Volume of the mixture of CO and CO₂ = 15 ml
- Volume of excess O₂ = V ml
- Volume after explosion = V + 12 ml

### Step 3: Determine the Volume of Gases After Reaction
After the reaction, the volume of gases can be expressed as:
\[ \text{Volume after explosion} = \text{Initial volume of gases} - \text{Volume of gases consumed} + \text{Volume of gases produced} \]

### Step 4: Calculate the Volume of CO and CO₂
Let’s denote:
- Volume of CO = x ml
- Volume of CO₂ = (15 - x) ml

From the reaction, we know:
- 1 mole of O₂ reacts with 2 moles of CO to produce 2 moles of CO₂.

### Step 5: Set Up the Equation
The total volume after the explosion can be expressed as:
\[ V + 12 = (15 - x) + (x - \frac{x}{2}) + (V - \frac{x}{2}) \]
This simplifies to:
\[ V + 12 = 15 + V - x \]

### Step 6: Solve for x
Rearranging the equation gives:
\[ x = 3 \text{ ml} \]
This means the volume of CO in the original mixture is 3 ml.

### Step 7: Calculate the Volume of CO₂
Substituting x back into the equation for CO₂:
\[ \text{Volume of CO₂} = 15 - x = 15 - 3 = 12 \text{ ml} \]

### Step 8: Determine the Residual Volume for 25 ml of Original Mixture
Now, if we take 25 ml of the original mixture, we need to find out how much CO is in that volume:
\[ \text{Volume of CO in 25 ml} = \frac{3}{15} \times 25 = 5 \text{ ml} \]

### Step 9: Calculate the Residual Volume After Alkali Treatment
When the 25 ml mixture is treated with alkali, CO will react with the alkali, and CO₂ will not be affected. Therefore, the volume of CO that reacts will be:
- Volume of CO remaining = 5 ml (initial) - 5 ml (reacted) = 0 ml
- Volume of CO₂ = 12 ml (remains unchanged)

Thus, the total residual volume after alkali treatment will be:
\[ \text{Residual Volume} = 0 \text{ ml (CO)} + 12 \text{ ml (CO₂)} = 12 \text{ ml} \]

### Final Answer
The residual volume after exposing 25 ml of the original mixture to an alkali is **12 ml**.

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