Answer:
1.44 L
Explanation:
According with Ideal gas law, it can be represented the dependencies between temperature, pressure, volume and molar amount of a ideal gas as follows:
[tex]PV=nRT[/tex]
Where:
[tex]P=Pressure\\ V=Volume\\n=Molar~amount\\T=Temperature\\R=Ideal~gas~Constant[/tex]
In this case the gas is contained in a balloon with a initial pressure, volume, molar amount and temperature ([tex]P_{1}, V_{1}, n_{1},T_{1}[/tex]) and changes to a second state with a final pressure, volume, molar amount and temperature ([tex]P_{2}, V_{2}, n_{2},T_{2}[/tex]). As we know, R is the Ideal Gas Constant and do not change with the state changes, then it is possible to obtain the equation:
[tex]\frac{P_{1}V_{1}}{n_{1}T_{1}}=R=\frac{P_{2}V_{2}}{n_{2}T_{2}}[/tex]
But the state change proceed at constant temperature and molar amount, then [tex]T_{1}=T_{2}[/tex] and [tex]n_{1}=n_{2}[/tex] and replacing in the previews equation we obtain:
[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]
So we can obtain the final Volume as follows:
[tex]\frac{P_{1}V_{1}}{P_{2}}=V_{2}= \frac{1.05(atm)*3.78(L)}{2.75(atm)}}=1.44(L)[/tex]
