Which one of the following volume (V)- temperature (T) plots represents the behaviour of one mole of an ideal gas at one atmosphere?

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining which volume (V) - temperature (T) plot represents the behavior of one mole of an ideal gas at one atmosphere, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature (in Kelvin)

### Step 2: Substitute Known Values
In this case, we have:
- \( n = 1 \) mole
- \( P = 1 \) atm
- \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
- We need to find \( V \) at a specific temperature.

### Step 3: Rearrange the Ideal Gas Law
Rearranging the ideal gas law to solve for volume \( V \):
\[ V = \frac{nRT}{P} \]

### Step 4: Calculate Volume at a Given Temperature
Assuming we want to find the volume at a temperature of \( T = 373 \) K:
\[ V = \frac{(1 \, \text{mol})(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1})(373 \, \text{K})}{1 \, \text{atm}} \]

### Step 5: Perform the Calculation
Calculating the volume:
\[ V = \frac{(1)(0.0821)(373)}{1} \]
\[ V = 30.58 \, \text{L} \]
This can be approximated to:
\[ V \approx 30.6 \, \text{L} \]

### Step 6: Analyze the Graphs
Now, we need to check the given volume-temperature plots to find which one corresponds to \( V = 30.6 \, \text{L} \) at \( T = 373 \, \text{K} \).

### Step 7: Identify the Correct Plot
Look for the plot that shows a point at \( (373 \, \text{K}, 30.6 \, \text{L}) \). The correct graph will show this specific volume at the specified temperature.

### Conclusion
The plot that correctly represents the behavior of one mole of an ideal gas at one atmosphere, with the calculated volume of approximately 30.6 liters at 373 Kelvin, is the answer.

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