Question

Diethyl ether (C2H5 )2O vaporizes at room temperature. If the vapor exerts a pressure of 233 mm Hg in a flask at 25 °C, what is the density of the vapor?​

Answer 1

Answer: The density of the given vapor is 0.939 g/L.

Explanation:

Given: Pressure = 233 mm Hg (1 mm Hg = 0.00131579 atm) = 0.31 atm

Temperature = $25^{o}C$ = (25 + 273) K = 298 K

According to the ideal gas equation,

$PV = \frac{m}{M}RT$

where,

P = pressure

V = volume

m = mass

M = molar mass

R = gas constant = 0.0821 L atm/mol K

T = temperature

This formula can be re-written as follows.

$PM = \frac{m}{V}RT$    (where, $Density = \frac{mass (m)}{Volume (V)}$ )

Hence, formula used to calculate density of diethy ether (molar mass = 74.12 g/mol) vapor is as follows.

$d = \frac{PM}{RT}$

Substitute values into the above formula as follows.

$d = \frac{PM}{RT}\\= \frac{0.31 atm \times 74.12 g/mol}{0.0821 L atm/mol K \times 298 K}\\= \frac{22.9772}{24.4658}\\= 0.939 g/L$

Thus, we can conclude that the density of the given vapor is 0.939 g/L.