Question

A 19.2g quantity of dry ice (solid carbon dioxide) is allowed to sublime (evaporate) in an apparatus. Calculate the expansion work done against a constant external pressure of 0.995 atm and at a constant temperature of 22 degrees C. Assume that the initial volume of dry ice is negligible and that CO2 behaves like an ideal gas.

Answer 1

Answer : The expansion work done against a constant external pressure is, -1063.65 J

Explanation :

First we have to calculate the moles of dry ice $(CO_2)$.

$\text{Moles of }CO_2=\frac{\text{Mass of }CO_2}{\text{Molar mass of }CO_2}$

Given:

Molar mass of $CO_2$ = 44 g/mole

Mass of $CO_2$ = 19.2 g

Now put all the given values in the above expression, we get:

$\text{Moles of }CO_2=\frac{19.2g}{44g/mol}=0.436mol$

Now we have to calculate the volume of dry ice.

Using ideal gas equation:

$PV=nRT$

where,

P = Pressure of $CO_2$ gas = 0.995 atm

V = Volume of $CO_2$ gas = ?

n = number of moles $CO_2$ = 0.436 mole

R = Gas constant = $0.0821L.atm/mol.K$

T = Temperature of $CO_2$ gas = $22^oC=273+22=295K$

Putting values in above equation, we get:

$0.995atm\times V=0.436mole\times (0.0821L.atm/mol.K)\times 295K$

$V=10.6L$

As initially, volume of dry ice is negligible. So,

Volume expanded = Volume of dry ice

Thus,

Expansion work = -(Pressure × Volume)

Expansion work = -0.995 atm × 10.6 L

Expansion work = -10.5 L.atm

Conversion used : (1 L.atm = 101.3 J)

Expansion work = -10.5 × 101.3 = -1063.65 J

Therefore, the expansion work done against a constant external pressure is, -1063.65 J