Respuesta :
Answer: The density of argon gas is [tex]0.0163g/cm^3[/tex]
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 argon = 39.95 g/mol
R = Gas constant = [tex]0.08206\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the gas = [tex]25^oC=[25+273]K=298K[/tex]
P = pressure of the gas = 10.0 atm
Putting values in equation 1, we get:
[tex]10.0atm\times 39.95g/mol=d\times 0.08206\text{ L atm }mol^{-1}K^{-1}\times 298K\\\\d=16.3g/L[/tex]
Converting the calculated density into [tex]g/cm^3[/tex], we use the conversion factor:
[tex]1L=1000cm^3[/tex]
Converting the density into [tex]g/cm^3[/tex], we get:
[tex]\Rightarrow \frac{16.3g}{L}\times (\frac{1L}{1000cm^3})=0.0163g/cm^3[/tex]
Hence, the density of argon gas is [tex]0.0163g/cm^3[/tex]
