At high temperature, `S_(4)N_(4)` decomposes into sulphur vapour and nitrogen. If 1 mL of `S_(4)N_(4)` is decomposed and 2.5 mL of mixture are obtained, the forinula of sulphur vapour is

Options

A. `S_(2)`
B. `S_(4)`
C. `S_(6)`
D. `S_(8)`

Answer

To solve the problem, we need to analyze the decomposition reaction of \( S_4N_4 \) and determine the formula of the sulfur vapor produced. Here’s a step-by-step breakdown of the solution:

### Step 1: Write the decomposition reaction
The decomposition of \( S_4N_4 \) can be represented as:
\[ S_4N_4 \rightarrow \text{Sulfur vapor} + \text{Nitrogen} \]

### Step 2: Understand the volume relationship
According to the problem, when 1 mL of \( S_4N_4 \) is decomposed, a total of 2.5 mL of gas mixture is produced. This means that the total volume of gases (sulfur vapor + nitrogen) after decomposition is 2.5 mL.

### Step 3: Determine the volume of nitrogen produced
From the video transcript, we know that the volume of nitrogen produced is 2 mL. Therefore, we can write:
\[ \text{Volume of } N_2 = 2 \text{ mL} \]

### Step 4: Calculate the volume of sulfur vapor
Since the total volume of the mixture is 2.5 mL, we can find the volume of sulfur vapor using the equation:
\[ \text{Volume of mixture} = \text{Volume of } N_2 + \text{Volume of sulfur vapor} \]
Substituting the known values:
\[ 2.5 \text{ mL} = 2 \text{ mL} + \text{Volume of sulfur vapor} \]
Thus, we find:
\[ \text{Volume of sulfur vapor} = 2.5 \text{ mL} - 2 \text{ mL} = 0.5 \text{ mL} \]

### Step 5: Set up the stoichiometric relationship
Let’s denote the formula of sulfur vapor as \( S_x \). The stoichiometry of the reaction can be expressed as:
\[ S_4N_4 \rightarrow x \text{ mL of } S_x + 2 \text{ mL of } N_2 \]
From the volumes, we can relate the volumes of sulfur and nitrogen produced:
- For every 1 mL of \( S_4N_4 \) decomposed, we have:
- 2 mL of \( N_2 \)
- 0.5 mL of \( S_x \)

### Step 6: Relate the volumes to the stoichiometry
From the stoichiometry, we can set up the ratio:
\[ \frac{4}{x} = \frac{2}{0.5} \]
This simplifies to:
\[ \frac{4}{x} = 4 \]
Cross-multiplying gives:
\[ 4 = 4x \]
Thus:
\[ x = 1 \]

### Step 7: Determine the formula of sulfur vapor
Since we have \( x = 1 \), we can deduce that the formula of sulfur vapor is:
\[ S_8 \]
This means that the sulfur vapor produced is in the form of \( S_8 \).

### Final Answer
The formula of sulfur vapor is \( S_8 \).

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