Hello!
The answer is:
The new volume is 2.84 L.
[tex]V_{2}=2.84L[/tex]
Why?
To solve the problem, we need to remember what STP means. STP means that the gas is at standard temperature and pressure, or 273.15 K (0°C) and 1 atm.
Also, we need to use the Combined Gas Law, since the temperature, the pressure and the volume are being changed.
The Combined Gas Law establishes a relationship between the temperature, the pressure and the volume of an ideal gas using , Gay-Lussac's Law, Charles's Law, and Boyle's Law.
The law is defined by the following equation:
[tex]\frac{P_{1}V{1}}{T_{1}}=\frac{P_{2}V{2}}{T_{2}}[/tex]
Where,
[tex]P_{1}[/tex] is the first pressure.
[tex]V_{1}[/tex] is the first volume.
[tex]T_{1}[/tex] is the first temperature.
[tex]P_{2}[/tex] is the second pressure.
[tex]V_{2}[/tex] is the second volume.
[tex]T_{2}[/tex] is the second temperature.
So, we are given the following information:
[tex]V_{1}=2L\\P_{1}=1atm\\T_{1}=0\°C=273.15K\\P_{2}=80kPa=0.8atm\\T_{2}=37\°C=37+273=310K[/tex]
Then, isolating the new volume, and substituting, we have:
[tex]\frac{P_{1}V{1}}{T_{1}}=\frac{P_{2}V{2}}{T_{2}}\\\\V_{2}=\frac{P_{1}V{1}}{T_{1}}*\frac{T_{2}}{P_{2}}\\\\V_{2}=\frac{1atm*2L}{273.15K}*\frac{310K}{0.8kPa}=2.84L[/tex]
Hence, the new volume is 2.84 L.
[tex]V_{2}=2.84L[/tex]
Have a nice day!
