When 20 ml of methane and 20 ml of oxygen are exploded together and the reaction mixture is cooled to laboratory temperature. The resulting volume of the mixture is

Options

A. a. 40 ml
B. b. 20 ml
C. c. 30ml
D. d. 10ml

Answer

To solve the problem, we need to analyze the reaction between methane (CH₄) and oxygen (O₂) and determine the resulting volume after the reaction has occurred and the mixture has cooled to laboratory temperature.

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation**:
The combustion of methane can be represented by the following balanced equation:
\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
This equation shows that 1 mole of methane reacts with 2 moles of oxygen to produce 1 mole of carbon dioxide and 2 moles of water.

2. **Identify Initial Volumes**:
We are given:
- Volume of methane (CH₄) = 20 ml
- Volume of oxygen (O₂) = 20 ml

3. **Determine the Limiting Reactant**:
From the balanced equation, we see that 1 volume of CH₄ requires 2 volumes of O₂. Therefore, for 20 ml of CH₄, we would need:
\[ 20 \text{ ml CH}_4 \times 2 = 40 \text{ ml O}_2 \]
However, we only have 20 ml of O₂ available. Thus, O₂ is the limiting reactant.

4. **Calculate the Amount of Reactants Used**:
Since O₂ is the limiting reactant, we will use all of the 20 ml of O₂. According to the stoichiometry of the reaction:
- 2 ml of O₂ reacts with 1 ml of CH₄.
- Therefore, 20 ml of O₂ will react with:
\[ \frac{20 \text{ ml O}_2}{2} = 10 \text{ ml CH}_4 \]
This means that 10 ml of CH₄ will be consumed.

5. **Determine the Amount of Products Formed**:
From the balanced equation, for every 1 ml of CH₄ consumed, 1 ml of CO₂ is produced. Therefore, the amount of CO₂ produced from 10 ml of CH₄ is:
\[ 10 \text{ ml CO}_2 \]
Additionally, 20 ml of O₂ produces 20 ml of water (H₂O), but since water is a liquid at laboratory temperature, we will not consider its volume in the gas phase.

6. **Calculate the Final Volume of the Mixture**:
After the reaction, we have:
- Remaining CH₄ = Initial CH₄ - Consumed CH₄ = 20 ml - 10 ml = 10 ml
- Produced CO₂ = 10 ml
- Water is not counted in the gas volume.

Thus, the total volume of the gas mixture after the reaction is:
\[ \text{Total Volume} = \text{Remaining CH}_4 + \text{Produced CO}_2 = 10 \text{ ml} + 10 \text{ ml} = 20 \text{ ml} \]

### Final Answer:
The resulting volume of the mixture after the reaction and cooling to laboratory temperature is **20 ml**.

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