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 = $\frac{742}{760}=0.976atm$    $(1atm=760torr)$

Final pressure = 795 torr = $\frac{795}{760}=1.046atm$

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

$P\propto \frac{1}{V}$

or,  $\frac{P_1}{P_2}=\frac{V_2}{V_1}$

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

$\frac{P_1}{P_2}=\frac{V_2}{V_1}$

$\frac{0.976atm}{1.046atm}=\frac{V_2}{0.5L}$

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.

$P\propto \frac{1}{V}$   (At constant temperature and number of moles)

Thus

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

$742torr\times 500ml=795torr\times V_2$

$V_2=466.67ml$