Respuesta :
Explanation:
According to ideal gas equation, the product of pressure and volume equals to the product of number of moles, gas constant and temperature.
Mathematically, PV = nRT
Since, it is given that pressure is constant and Charle's law states that at constant pressure volume of an ideal gas is directly proportional to the absolute temperature.
Therefore, [tex]V \propto T[/tex]
[tex]\frac{V}{T}[/tex] = constant
So, number of moles will also be constant then. Hence, the formula will be as follows.
[tex]\frac{V_{1}}{T_{1}}[/tex] = [tex]\frac{V_{2}}{T_{2}}[/tex]
As it is given that [tex]V_{1}[/tex] is 9.53 L, [tex]V_{2}[/tex] is 4.36 L, [tex]T_{1}[/tex] is [tex]215^{o}C[/tex] that is also equal to (215 + 273) K = 488 K.
Now, putting these values into the formula as follows.
[tex]\frac{V_{1}}{T_{1}}[/tex] = [tex]\frac{V_{2}}{T_{2}}[/tex]
[tex]\frac{9.53 L}{488 K}[/tex] = [tex]\frac{4.36 L}{T_{2}}[/tex]
[tex]T_{2}[/tex] = 223.26 K
Temperature in degree celsius will be (223.26 K - 273 K) = [tex]-49.73^{o}C[/tex]
Thus, we can conclude that temperature (in °C) is needed to reduce the volume to 4.36 L is [tex]-49.73^{o}C[/tex].
