A sample of coal gas contains 50% hydrogen, 30% methane, 14% CO and 6% `C_2H_4` 100 ml of this coal gas is mixed with 150 ml of oxygen and the mixture is exploded. What will be the composition of the resulting gas when it is to room temperature ?

Options

A. `52.81 %O_2 & 47.19% CO_2`
B. `47.33% & 52.67 % CO_2`
C. `41.67% O_2 & 58.33 CO_2`
D. `33.87% O_2 & 66.13 % CO_2`

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the volumes of each component in the coal gas.
The coal gas composition is given as:
- 50% Hydrogen (H₂)
- 30% Methane (CH₄)
- 14% Carbon Monoxide (CO)
- 6% Ethylene (C₂H₄)

Since we have 100 ml of coal gas:
- Volume of H₂ = 50% of 100 ml = 50 ml
- Volume of CH₄ = 30% of 100 ml = 30 ml
- Volume of CO = 14% of 100 ml = 14 ml
- Volume of C₂H₄ = 6% of 100 ml = 6 ml

### Step 2: Write the balanced chemical reactions for each component.
1. **Hydrogen combustion:**
\[ 2H_2 + O_2 \rightarrow 2H_2O \]
For 50 ml of H₂, we need 25 ml of O₂ (since 2 ml of H₂ reacts with 1 ml of O₂).

2. **Methane combustion:**
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]
For 30 ml of CH₄, we need 60 ml of O₂ (since 1 ml of CH₄ reacts with 2 ml of O₂).

3. **Carbon monoxide combustion:**
\[ 2CO + O_2 \rightarrow 2CO_2 \]
For 14 ml of CO, we need 7 ml of O₂ (since 2 ml of CO reacts with 1 ml of O₂).

4. **Ethylene combustion:**
\[ C_2H_4 + 3O_2 \rightarrow 2CO_2 + 2H_2O \]
For 6 ml of C₂H₄, we need 18 ml of O₂ (since 1 ml of C₂H₄ reacts with 3 ml of O₂).

### Step 3: Calculate the total volume of O₂ required.
Now, we sum the volumes of O₂ required for each reaction:
- From H₂: 25 ml
- From CH₄: 60 ml
- From CO: 7 ml
- From C₂H₄: 18 ml

Total O₂ required = 25 ml + 60 ml + 7 ml + 18 ml = 110 ml

### Step 4: Determine the unused O₂.
We started with 150 ml of O₂, and we used 110 ml.
Unused O₂ = 150 ml - 110 ml = 40 ml

### Step 5: Calculate the volume of CO₂ produced.
Now, we calculate the volume of CO₂ produced from each component:
1. From CH₄: 30 ml of CH₄ produces 30 ml of CO₂.
2. From CO: 14 ml of CO produces 7 ml of CO₂.
3. From C₂H₄: 6 ml of C₂H₄ produces 12 ml of CO₂.

Total CO₂ produced = 30 ml + 7 ml + 12 ml = 49 ml

### Step 6: Summarize the final composition of the resulting gas.
After the explosion, the resulting gas composition at room temperature will be:
- Unused O₂: 40 ml
- CO₂ produced: 49 ml

### Final Answer:
The composition of the resulting gas will be:
- 40 ml of O₂
- 49 ml of CO₂

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