Which of the following volume-temperature `(V-I)` plots represents the behaviour of `1 "mole"` of an ideal gas at the atmospheric pressure?

Options

A.
B.
C.
D.

Answer

To solve the question regarding which volume-temperature (V-T) plot represents the behavior of 1 mole of an ideal gas at atmospheric pressure, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The behavior of an ideal gas can be described by the Ideal Gas Law, which states:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Identify Standard Conditions
At Standard Temperature and Pressure (STP), which is defined as:
- Temperature \( T = 273 \, K \)
- Pressure \( P = 1 \, atm \)

1 mole of an ideal gas occupies approximately:
\[ V = 22.4 \, L \]

### Step 3: Calculate Volume at Different Temperatures
We need to analyze the relationship between volume and temperature. According to Charles's Law, the volume of an ideal gas is directly proportional to its temperature when pressure is constant:
\[ V \propto T \]

### Step 4: Analyze Given Data
We are given:
- At STP (273 K), the volume is 22.4 L.
- At a volume of 30.6 L, we need to find the corresponding temperature.

Using the direct proportionality:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 = 22.4 \, L \)
- \( T_1 = 273 \, K \)
- \( V_2 = 30.6 \, L \)
- \( T_2 = ? \)

### Step 5: Calculate the Temperature for 30.6 L
Rearranging the equation gives:
\[ T_2 = \frac{V_2 \cdot T_1}{V_1} \]

Substituting the known values:
\[ T_2 = \frac{30.6 \, L \cdot 273 \, K}{22.4 \, L} \]

Calculating:
\[ T_2 = \frac{30.6 \cdot 273}{22.4} \approx 373 \, K \]

### Step 6: Determine the Correct V-T Plot
Since we have established that the volume is directly proportional to temperature, we can eliminate any plots that show an inverse relationship.

- **Graph A**: Shows a direct relationship and passes through the point (22.4 L, 273 K) and (30.6 L, 373 K).
- **Graph B**: Shows an inverse relationship (not suitable).
- **Graph C and D**: Need to be checked against the calculated values.

### Conclusion
The correct V-T plot that represents the behavior of 1 mole of an ideal gas at atmospheric pressure is **Graph A**.