Of course! Let's determine the volume of an oxygen gas sample that is initially at 200 ml and 100°C, when the temperature is changed to 0°C, assuming the pressure remains constant.
### Step-by-Step Solution
1. Initial Conditions:
- Initial volume ([tex]\( V_1 \)[/tex]) = 200 ml
- Initial temperature ([tex]\( T_1 \)[/tex]) = 100°C
2. Final Conditions:
- Final temperature ([tex]\( T_2 \)[/tex]) = 0°C
3. Convert Temperatures to Kelvin:
In the equation for Charles's Law, temperatures should be in Kelvin.
- To convert from Celsius to Kelvin, use the formula: [tex]\( K = °C + 273.15 \)[/tex].
- [tex]\( T_1 \)[/tex] (Initial temperature in Kelvin): 100°C + 273.15 = 373.15 K
- [tex]\( T_2 \)[/tex] (Final temperature in Kelvin): 0°C + 273.15 = 273.15 K
4. Charles's Law:
Charles’s Law states that [tex]\( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)[/tex], where:
- [tex]\( V_1 \)[/tex] and [tex]\( V_2 \)[/tex] are the initial and final volumes respectively,
- [tex]\( T_1 \)[/tex] and [tex]\( T_2 \)[/tex] are the initial and final temperatures respectively.
5. Set Up the Equation:
[tex]\[
\frac{200 \, \text{ml}}{373.15 \, \text{K}} = \frac{V_2}{273.15 \, \text{K}}
\][/tex]
6. Solve for [tex]\( V_2 \)[/tex]:
Rearrange the equation to solve for the final volume [tex]\( V_2 \)[/tex]:
[tex]\[
V_2 = 200 \, \text{ml} \times \frac{273.15 \, \text{K}}{373.15 \, \text{K}}
\][/tex]
7. Calculate [tex]\( V_2 \)[/tex]:
Simplify the expression to find the final volume:
[tex]\[
V_2 = 200 \, \text{ml} \times \frac{273.15}{373.15} \approx 146.402 \, \text{ml}
\][/tex]
### Conclusion
The volume of the oxygen gas at 0°C, assuming the pressure remains constant, would be approximately 146.4 ml.
