The volume of a given mass of a gas is 100ml at 100°C. If pressure is kept constant at what temperature will the sample have the volume of 200ml?

Options

A. `50^(@)` C
B. `473^(@)` C
C. `200^(@)` C
D. `400^(@)` C

Answer

To solve the problem, we will use Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). The formula for Charles's Law is:

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial volume, \( V_1 = 100 \, \text{ml} \)
- Initial temperature, \( T_1 = 100^\circ C \)
- Final volume, \( V_2 = 200 \, \text{ml} \)

2. **Convert the initial temperature to Kelvin:**
- The conversion from Celsius to Kelvin is done using the formula:
\[ T(K) = T(°C) + 273.15 \]
- Therefore,
\[ T_1 = 100 + 273.15 = 373.15 \, K \]

3. **Set up the equation using Charles's Law:**
- According to Charles's Law:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Plugging in the known values:
\[ \frac{100 \, \text{ml}}{373.15 \, K} = \frac{200 \, \text{ml}}{T_2} \]

4. **Cross-multiply to solve for \( T_2 \):**
- Cross-multiplying gives us:
\[ 100 \, \text{ml} \cdot T_2 = 200 \, \text{ml} \cdot 373.15 \, K \]
- Simplifying this:
\[ T_2 = \frac{200 \cdot 373.15}{100} \]

5. **Calculate \( T_2 \):**
- Performing the calculation:
\[ T_2 = 746.3 \, K \]

6. **Convert \( T_2 \) back to Celsius:**
- To convert Kelvin back to Celsius:
\[ T(°C) = T(K) - 273.15 \]
- Therefore,
\[ T_2 = 746.3 - 273.15 = 473.15^\circ C \]

### Final Answer:
The temperature at which the sample will have a volume of 200 ml is approximately \( 473^\circ C \).