Answer:
40 g/mol, Argon
Explanation:
We can find the number of moles of the gas by using the equation of state for an ideal gas:
[tex]pV=nRT[/tex]
where
[tex]p=101,300 Pa[/tex] is the pressure of the gas at STP
[tex]V=2.96 L = 2.96\cdot 10^{-3} m^3[/tex] is the volume of the gas
n is the number of moles
[tex]R=8.314 J/mol K[/tex] is the gas constant
[tex]T=0^{\circ}C=273 K[/tex] is the absolute temperature of the gas at STP
Solving for n, we find:
[tex]n=\frac{pV}{RT}=\frac{(101,300)(2.96\cdot 10^{-3})}{(8.314)(273)}=0.132 mol[/tex]
Now we can find the molar mass of the gas, which is given by
[tex]M_m=\frac{m}{n}[/tex]
where
m = 5.28 g is the mass of the gas
n = 0.132 mol is the number of moles
Substituting,
[tex]M_m=\frac{5.28}{0.132}=40 g/mol[/tex]
So, the gas in this problem is Argon, which has a molar mass of 40 g/mol.
