Answer :
Answer:
[tex]\bold{608.363\: L \approx V_2}[/tex]
Explanation:
Combined Gas Law
As the name suggests, the Combined Gas Law combines the three ideal gas laws: Boyle's, Charles', and Gay-Lussac's.
[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex],
where P is pressure (in atm), V is volume (in L), and T is temperature (in K).
[tex]\hrulefill[/tex]
Solving the Problem
We're given the
- initial pressure, volume, and temperature: [tex]P_1,\:V_1,\:T_1[/tex]
- the final pressure and temperature: [tex]P_2,\:T_2[/tex]
and we're asked to find the final volume: [tex]V_2[/tex].
[tex]\dotfill[/tex]
Converting Temperature to Kelvin (K)
Before we can plug and rearrange to find the value of the final volume, we must convert the temperatures to Kelvin (K) since we're given its Celsius form.
Using the Celsius to Kelvin formula, we can convert the two temperatures.
[tex]C+273.15=K[/tex]
[tex]39.3+273.15=312.45^\circ K[/tex]
[tex]1.5+273.15=274.65^\circ K[/tex]
[tex]\dotfill[/tex]
Putting it Together
Now, we can plug and rearrange!
[tex]\dfrac{(1.217)(281.5)}{(312.45)} =\dfrac{(0.495)V_2}{(274.65)}[/tex]
[tex]\dfrac{(1.217)(281.5)(274.65)}{(312.45)(0.495)} =V_2[/tex]
(multiply both sides by the denominator; divide both sides by the numerator)
[tex]\boxed{608.363\: L \approx V_2}[/tex].
