Answer:
1) [tex]V_{1}[/tex]= 100ml = 0.1 L
2) [tex]P_{1}[/tex]= 50kPa
[tex]1) P_{2} =400 kPa\\2)V_{2} =?[/tex]
So,
[tex]P_{1}V_{1} = P_{2} V_{2}[/tex]
[tex]V_{2} = \frac{0.1 x 50}{400}[/tex]
[tex]V_{2} = 0.0125 L[/tex]
[tex]2) V_{1} = 100 mL = 0.1 L\\P_{1}= 103 kPa\\V_{2}=2 mL\\P_{2} =?\\[/tex]
[tex]P_{1} V_{1} =P_{2} V_{2}\\ P_{2}=\frac{0.1x103}{2}\\ P_{2}=5.15 kPa[/tex]
[tex]4) V_{1}=2 cm^{3} = 0.002 dm^3\\P_{1} =3 atm x 760 = 2280 torr\\P_{2} = 0.0200 atm x 760=15.2 torr[/tex]
Same, formula as above,
[tex]V_{2}=\frac{2280x0.002}{15.2}\\V_{2}=0.3 L[/tex]
[tex]7)V_{1}=325\\T_{1}=20^{0}C=293K\\ P_{1}=723 torr\\V_{2}=975L\\T_{2} = 20^0 C= 293K\\P_{2}=?[/tex]
By the formula,
[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}} \\P_{2} = \frac{723x325x293}{293x975}[/tex]
[tex]P_{2} =241 Torr[/tex]