Answer: 6.18 g/L
Explanation:
To calculate the density of gas, we use the equation given by ideal gas equation:
[tex]PV=nRT[/tex]
Number of moles (n) can be written as: [tex]n=\frac{m}{M}[/tex]
where, m = given mass
M = molar mass
[tex]PV=\frac{m}{M}RT\\\\PM=\frac{m}{V}RT[/tex]
where,
[tex]\frac{m}{V}=d[/tex] which is known as density of the gas
The relation becomes:
[tex]PM=dRT[/tex] .....(1)
We are given:
M = molar mass of [tex]SF_6[/tex] = 146.06 g/mol
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the gas = [tex]15^oC=[15+273]K=288K[/tex]
P = pressure of the gas = 1 atm
Putting values in equation 1, we get:
[tex]1atm\times 146.06g/mol=d\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 288K\\\\d=6.18g/L[/tex]
Thus density of sulfur hexafluoride gas at exactly 15°C and exactly 1atm is 6.18g/L
