Question

On your way out of the lab, you shut the door of the temperature controlled, airtight volatiles closet but accidentally left the lid off the brand new, completely full 200L drum of diethyl ether. The volatiles closet is maintained at a steady 25°C and is 4m by 6m by 3m. The vapor pressure of diethyl ether is 470 mm Hg at 25°C. The molar mass of diethyl ether is 74 g/mol and the density is 713 kg/m³.

a. What would the pressure in the closet be (in atm) if all the diethyl ether evaporated and there was no air present in the closet when you shut the door?

b. Will all the diethyl ether evaporate? Why or why not?

Answer 1

ANSWER Q.a. :

GIVEN :

1. Density = d = 713 kg/m3

2. Volume diethyl ether = V1 = 200 L = 200 m3

3. Molar mass = m = 74 g/mol

4. Volume of Closet = V2 = 4m x 6m x 3m = 72m3

Density = Mass/ Volume

D = M / V1

Here Volume diethyl ether = 200 L = 200 m3

Density = Mass/ Volume = 713 kg/m3.

Mass = M = 713 kg/m3 x 200 L = 142600 Kg

To calculate n = Moles of diethyl ether = M in gram

Moles = 142600*1000/74 = 1927027 moles per litre

n = number of moles of diethyl ether

n = 1927027 moles per litre

PV = nRT

P = pressure = nRT/V

Here,

1. R = 8.314 J/mol·K.

2. T = (25+273.15) K

P = [8.314 J/mol·K. x 1927027 moles x (25+273.15)K ] /72

P = 6634376 Pa = 66343.76 KPa

P = 66343.76 KPa = 65.47 atm pressure is present in the closet be (in atm) if all the 200 Litre diethyl ether evaporated and there was no air present in the closet when you shut the door.

ANSWER Q.b. :

All the diethyl ether will evaporate. Main condition for evaporation is ,

If the vapor pressure of a liquid is in the equilibrium pressure of a vapuor above its liquid ; that is, the pressure of the vapour of it self results in total evaporation of a liquid.

Here in this case vapour pressure of a Diethyl ether is 470 mm of Hg = 0.61 atm & pressure of a vapour above its vapour is 65.47 atm which is in equilibrium. Therefore all the diethyl ether will  evaporate.