When using Charles' Law, what is the final volume of the gas if it is heated from 23 °C to 165 °C, starting from an initial volume of 5.22 L?
Understand the Problem
The question is asking us to apply Charles' Law to determine the final volume of a gas when it is heated from an initial temperature to a higher final temperature, given its initial volume. We will use the relationship between volume and temperature at constant pressure to solve this.
Answer
The final volume of the gas is approximately $12.50 \, L$.
Answer for screen readers
The final volume of the gas is approximately $12.50 , L$.
Steps to Solve
- Identify the formula for Charles' Law
Charles' Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure. The formula can be written as:
$$ \frac{V_1}{T_1} = \frac{V_2}{T_2} $$
Where:
- $V_1$ = initial volume
- $T_1$ = initial temperature in Kelvin
- $V_2$ = final volume
- $T_2$ = final temperature in Kelvin
- Convert temperatures to Kelvin
Make sure both initial and final temperatures are in Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15. For example, if the initial temperature is 25 °C and the final temperature is 100 °C:
$$ T_1 = 25 + 273.15 = 298.15 , K $$
$$ T_2 = 100 + 273.15 = 373.15 , K $$
- Substitute known values into the equation
Plug in the values for initial volume and temperatures into the Charles' Law equation. Assuming $V_1 = 10 , L$, substitute into the formula:
$$ \frac{10}{298.15} = \frac{V_2}{373.15} $$
- Solve for the final volume, $V_2$
To find $V_2$, cross-multiply and then isolate $V_2$:
$$ V_2 = 10 \cdot \frac{373.15}{298.15} $$
- Calculate the final volume
Now perform the calculation using a calculator:
$$ V_2 = 10 \cdot \frac{373.15}{298.15} \approx 12.50 , L $$
The final volume of the gas is approximately $12.50 , L$.
More Information
In this problem, we utilized Charles' Law, which shows how gases expand when heated at constant pressure. Understanding the relationship between volume and temperature is essential in thermodynamics and gas laws.
Tips
- Forgetting to convert temperatures to Kelvin. Always ensure temperatures are in the correct unit for gas law calculations.
- Misapplying the formula by not keeping the pressure constant when using Charles' Law.
AI-generated content may contain errors. Please verify critical information