Question

Calculate the expansion work done against a constant external pressure of 0.995 atm and at a constant temperature of 19°C. Assume that the initial volume of dry ice is negligible and that CO2 behaves like an ideal gas.

Answer 1

This is an incomplete question, here is a complete question.

A 19.2 g 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 : The expansion work done is, -1058.33 J

Explanation :

First we have to calculate the volume of gas.

Using ideal gas equation:

$PV=nRT\\\\PV=\frac{w}{M}RT$

where,

P = pressure of gas = 0.995 atm

Conversion used : (1 atm = 760 torr)

V = volume of gas = ?

T = temperature of gas = $19^oC=273+19=292K$

R = gas constant = 0.0821 L.atm/mole.K

w = mass of gas = 19.2 g

M = molar mass of carbon dioxide gas = 44 g/mole

Now put all the given values in the ideal gas equation, we get:

$(0.995atm)\times V=\frac{19.2g}{44g/mole}\times (0.0821L.atm/mole.K)\times (292K)$

$V=\frac{19.2g}{44g/mole}\times \frac{(0.0821L.atm/mole.K)\times (292K)}{0.995atm}$

$V=10.5L$

Now we have to calculate the work done.

Formula used :

$w=-p\Delta V$

where,

w = work done

p = pressure of the gas = 0.995 atm

$\Delta V$ = volume = 10.5 L

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

$w=-p\Delta V$

$w=-(0.995atm)\times (10.5L)$

$w=-10.4475L.atm=-10.4475\times 101.3J=-1058.33J$

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

Thus, the expansion work done is, -1058.33 J