Which is correct curve for Charle's law, when the curve is plotted at 0.821 atm pressure for 10 mole ideal gas?

Options

A.
B.
C.
D.

Explanation

To solve the question regarding which curve is correct for Charles's law when plotted at 0.821 atm pressure for a 10 mole ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Charles's Law**:
Charles's Law states that for a fixed amount of gas at constant pressure, the volume (V) of the gas is directly proportional to its absolute temperature (T). Mathematically, this can be expressed as:
\[ V \propto T \quad \text{or} \quad V = kT \]
where \( k \) is a constant.

2. **Use the Ideal Gas Law**:
The ideal gas law is given by:
\[ PV = nRT \]
For this scenario, we know the pressure (P = 0.821 atm), the number of moles (n = 10), and the gas constant (R = 0.0821 L·atm/(K·mol)).

3. **Rearranging the Ideal Gas Law**:
Rearranging the ideal gas law for volume gives:
\[ V = \frac{nRT}{P} \]
Substituting the known values:
\[ V = \frac{10 \times 0.0821 \times T}{0.821} \]

4. **Calculate the Constant**:
Simplifying the equation:
\[ V = \frac{0.821T}{0.821} \quad \Rightarrow \quad V = 10 \times 0.1T \quad \Rightarrow \quad V = 1T \]
Thus, we can see that the slope \( k \) is equal to \( \frac{10 \times 0.0821}{0.821} \).

5. **Determine the Slope**:
The slope of the graph (which is \( \frac{V}{T} \)) is constant, and it indicates that as temperature increases, volume increases linearly.

6. **Graph Analysis**:
- **Option A**: If the graph shows \( V/T \) increasing, it is incorrect because \( V/T \) should be constant.
- **Option B**: If the graph shows a linear relationship between \( V \) and \( T \), it is correct as it reflects Charles's Law.
- **Option C**: If the graph shows \( V^2/T \) versus \( V \), it is incorrect as it does not represent a direct relationship.
- **Option D**: If the graph shows \( \log V \) versus \( \log T \), it is incorrect as it does not represent a linear relationship.

7. **Conclusion**:
The correct curve that represents Charles's Law at the given conditions is the one that shows a direct linear relationship between volume (V) and temperature (T), which corresponds to **Option B**.