Respuesta :
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.
[tex]P\propto \frac{1}{V}[/tex] (At constant temperature and number of moles)
Thus
[tex]P_1V_1=P_2V_2[/tex] [according to Boyle's law]
[tex]742torr\times 500ml=795torr\times V_2[/tex]
[tex]V_2=466.67ml[/tex]
Answer : The volume of [tex]CO_2[/tex] will be 0.4665 L
Solution : Given,
Initial volume = 500 ml = 0.5 L (1 L = 1000 ml)
Initial pressure = 742 torr = [tex]\frac{742}{760}=0.976atm[/tex] [tex](1atm=760torr)[/tex]
Final pressure = 795 torr = [tex]\frac{795}{760}=1.046atm[/tex]
According to the Boyle's law, the pressure of the gas is inversely proportional to the volume of the gas at constant temperature.
[tex]P\propto \frac{1}{V}[/tex]
or, [tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex]
where,
[tex]P_1[/tex] = initial pressure of the gas
[tex]P_2[/tex] = final pressure of the gas
[tex]V_1[/tex] = initial volume of the gas
[tex]V_2[/tex] = final volume of the gas
Now put all the given values in the above formula, we get
[tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex]
[tex]\frac{0.976atm}{1.046atm}=\frac{V_2}{0.5L}[/tex]
By rearranging the terms, we get the final volume of the gas.
[tex]V_2=0.4665L[/tex]
Therefore, the volume of [tex]CO_2[/tex] will be 0.4665 L
