To determine the molecular formula of the organic compound A from the given data, we can follow these steps:
### Step 1: Analyze the combustion reaction
The combustion of a hydrocarbon (organic compound A) in the presence of oxygen (O₂) produces carbon dioxide (CO₂), water (H₂O), and nitrogen (N₂). The general reaction can be represented as:
\[ \text{C}_x\text{H}_y\text{N}_z + O_2 \rightarrow CO_2 + H_2O + N_2 \]
### Step 2: Write down the volumes given
From the problem, we have the following volumes:
- Volume of CO₂ = 16 ml
- Volume of H₂O = 24 ml
- Volume of N₂ = 8 ml
- Total volume of the gaseous mixture = 36 ml
### Step 3: Calculate the volume of oxygen required
According to the stoichiometry of the combustion reaction:
- 1 mole of CO₂ corresponds to 1 mole of carbon (C).
- 1 mole of H₂O corresponds to 2 moles of hydrogen (H).
- The nitrogen does not participate in the combustion but is present in the organic compound.
Using the volumes, we can find the moles of each component:
- Moles of CO₂ = 16 ml
- Moles of H₂O = 24 ml
- Moles of N₂ = 8 ml
### Step 4: Determine the moles of oxygen needed
From the combustion stoichiometry:
- For every 1 mole of CO₂ produced, 1 mole of O₂ is needed.
- For every 1 mole of H₂O produced, 0.5 moles of O₂ is needed.
Thus, the total moles of O₂ required can be calculated as:
\[
\text{Moles of O}_2 = \text{Moles of CO}_2 + 0.5 \times \text{Moles of H}_2O
\]
Substituting the values:
\[
\text{Moles of O}_2 = 16 + 0.5 \times 24 = 16 + 12 = 28 \text{ ml}
\]
### Step 5: Calculate the volume of the organic compound A
The volume of the organic compound A can be calculated as:
\[
\text{Volume of A} = \text{Total volume} - \text{Volume of O}_2
\]
Substituting the values:
\[
\text{Volume of A} = 36 - 28 = 8 \text{ ml}
\]
### Step 6: Determine the number of atoms (C, H, N)
Now we can find the number of carbon (C), hydrogen (H), and nitrogen (N) atoms in the organic compound A:
- From CO₂ (16 ml), we have 16 moles of C, which corresponds to:
\[
x = \text{Moles of C} = 16 \text{ ml of CO}_2 \rightarrow x = 2 \text{ (since 8 ml of A gives 2 moles of C)}
\]
- From H₂O (24 ml), we have 24 moles of H, which corresponds to:
\[
y = \text{Moles of H} = 2 \times \text{Moles of H}_2O = 24 \text{ ml} \rightarrow y = 6 \text{ (since 8 ml of A gives 6 moles of H)}
\]
- From N₂ (8 ml), we have 8 moles of N, which corresponds to:
\[
z = \text{Moles of N} = 2 \times \text{Moles of N}_2 = 8 \text{ ml} \rightarrow z = 2 \text{ (since 8 ml of A gives 2 moles of N)}
\]
### Step 7: Write the molecular formula
Combining the values of x, y, and z, we get the molecular formula:
\[
\text{Molecular formula} = \text{C}_2\text{H}_6\text{N}_2
\]
### Final Answer
The molecular formula of the compound A is \( \text{C}_2\text{H}_6\text{N}_2 \).
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