At a temperature T K, the pressure of 4.0g argon in a bulb is p. The bulb is put in a bath having temperature higher by 50K than the first one 0.8g of argon gas had to be removed to maintained original pressure. The temperature T is equal to

Options

A. 510 K
B. 200 K
C. 100 K
D. 73 K

Explanation

To solve the problem, we will use the ideal gas law and the concept of moles of gas. The relationship between the number of moles, temperature, and pressure will help us find the initial temperature \( T \).

### Step-by-Step Solution:

1. **Identify the Molar Mass of Argon**:
The molar mass of argon (Ar) is approximately 40 g/mol.

2. **Calculate Initial Moles of Argon**:
The initial mass of argon is 4.0 g.
\[ n_1 = \frac{\text{mass}}{\text{molar mass}} = \frac{4.0 \, \text{g}}{40 \, \text{g/mol}} = 0.1 \, \text{mol} \]

3. **Determine the Final Moles of Argon**:
After removing 0.8 g of argon, the remaining mass is:
\[ \text{Remaining mass} = 4.0 \, \text{g} - 0.8 \, \text{g} = 3.2 \, \text{g} \]
Now, calculate the final number of moles:
\[ n_2 = \frac{3.2 \, \text{g}}{40 \, \text{g/mol}} = 0.08 \, \text{mol} \]

4. **Set Up the Relationship Between Initial and Final States**:
According to the ideal gas law, we can express the relationship between the initial and final states as:
\[ n_1 T_1 = n_2 T_2 \]
Where:
- \( T_1 = T \) (initial temperature)
- \( T_2 = T + 50 \, \text{K} \) (final temperature)

5. **Substitute Values into the Equation**:
Substitute \( n_1 \), \( n_2 \), \( T_1 \), and \( T_2 \) into the equation:
\[ 0.1 \, \text{mol} \cdot T = 0.08 \, \text{mol} \cdot (T + 50) \]

6. **Expand and Rearrange the Equation**:
Expanding the right side:
\[ 0.1T = 0.08T + 4 \]
Rearranging gives:
\[ 0.1T - 0.08T = 4 \]
\[ 0.02T = 4 \]

7. **Solve for \( T \)**:
\[ T = \frac{4}{0.02} = 200 \, \text{K} \]

### Final Answer:
The initial temperature \( T \) is \( 200 \, \text{K} \).

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