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?

Steps to Solve

1. 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

2. 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:

$$ T_1 = 25 + 273.15 = 298.15 , K $$
$$ T_2 = 100 + 273.15 = 373.15 , K $$

3. 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:

$$ \frac{10}{298.15} = \frac{V_2}{373.15} $$

4. Solve for the final volume, $V_2$

To find $V_2$, cross-multiply and then isolate $V_2$:

$$ V_2 = 10 \cdot \frac{373.15}{298.15} $$

5. Calculate the final volume

Now perform the calculation using a calculator:

$$ V_2 = 10 \cdot \frac{373.15}{298.15} \approx 12.50 , L $$