Question

A container holds 500. ML of CO2 at 20.° C and 742 torr. What will be the volume of the CO2 if the pressure is increased to 795 torr?

Answer 1

Answer : The volume of
`CO_2` will be 0.4665 L

Solution : Given,

Initial volume = 500 ml = 0.5 L (1 L = 1000 ml)

Initial pressure = 742 torr =
`(742)/(760)=0.976atm`
`(1atm=760torr)`

Final pressure = 795 torr =
`(795)/(760)=1.046atm`

According to the Boyle's law, the pressure of the gas is inversely proportional to the volume of the gas at constant temperature.

`P\propto (1)/(V)`

or,
`(P_1)/(P_2)=(V_2)/(V_1)`

where,

`P_1` = initial pressure of the gas

`P_2` = final pressure of the gas

`V_1` = initial volume of the gas

`V_2` = final volume of the gas

Now put all the given values in the above formula, we get

`(P_1)/(P_2)=(V_2)/(V_1)`

`(0.976atm)/(1.046atm)=(V_2)/(0.5L)`

By rearranging the terms, we get the final volume of the gas.

`V_2=0.4665L`

Therefore, the volume of
`CO_2` will be 0.4665 L

Answer 2

Answer: 466.67 ml

Explanation:

Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

`P\propto (1)/(V)` (At constant temperature and number of moles)

Thus

`P_1V_1=P_2V_2` [according to Boyle's law]

`742torr* 500ml=795torr* V_2`

`V_2=466.67ml`