Answer:
The volume of the ideal gas on another planet will be 6.7 m³.
Explanation:
We can find the volume occupied by the ideal gas on another planet by using the Ideal Gas Law:
[tex] PV = nRT [/tex]
Where:
P: is the pressure
V: is the volume
n: is the number of moles
R: is the gas constant = 8.206x10⁻⁵ m³ atm K⁻¹mol⁻¹
T: is the temperature
Since the gas occupies a volume of 8.7 m³ with a pressure of 6 atm and temperature 4.8 °C on earth, we have the following number of moles:
[tex] n = \frac{PV}{RT} = \frac{6 atm*8.7 m^{3}}{8.206 \cdot 10^{-5} m^{3}atm/(Kmol)*(4.8 + 273)K} = 2289.9 moles [/tex]
Now we can calculate the volume occupied by the ideal gas on another planet:
[tex] V = \frac{nRT}{P} [/tex]
With T = 8.7 °C and P = 7.9 atm
[tex] V = \frac{2289.9 moles*8.206 \cdot 10^{-5} m^{3}atm/(Kmol)*(8.7 + 273)K}{7.9 atm} = 6.7 m^{3} [/tex]
Therefore, the volume of the ideal gas on another planet will be 6.7 m³.
I hope it helps you!
