What is the density of Freon-11 (CFCl3) at 166 degrees Celsius and 5.92 atm?

Question

Wyatt Adkins · Accepted Answer

The density of Freon-11 is 22.6 g/L.

Freon-11 is a compound with formula #"CFCl"_3#. Its chemical name is trichlorofluoromethane. We can use the Ideal Gas Law to determine its density. #color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "# Since #n = m/M#, we can substitute this to get #pV = (m/M)RT# We can rearrange this to #pM = m/VRT# But #"density"= "mass"/"volume"# or #color(brown)(bar(ul(|color(white)(a/a)ρ = m/Vcolor(white)(a/a)|)))" "# ∴ #pM = ρRT# and #color(brown)(bar(ul(|color(white)(a/a)ρ = (pM)/(RT)color(white)(a/a)|)))" "# In your problem, #p = "5.92 atm"# #M = "137.37 g/mol"# #R = "0.082 06 L·atm·K"^"-1""mol"^"-1"# #T = "166 °C" = "439.15 K"# ∴ #ρ = (5.92color(red)(cancel(color(black)("atm"))) × 137.37color(white)(l) "g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06 L"·color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1"))) × 439.15color(red)(cancel(color(black)("K")))) = "22.6 g/L"#

Jose Ayala · Answer

undefined To calculate the density of Freon-11 (CFCl3) at 166 degrees Celsius and 5.92 atm, you can use the ideal gas law. The molar mass of CFCl3 is 137.37 g/mol. The ideal gas law equation is: 
$$PV = nRT$$
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
To find the number of moles, use the formula: 
$$n = \frac{PV}{RT}$$
Then, to find the density, use the formula: 
$$Density = \frac{mass}{volume}$$
$$mass = n \times \text{molar mass of CFCl3}$$
$$volume = \frac{RT}{P}$$
Substitute the values into the formulas and solve for density.