Question

A 1.25g sample of dry ice is added to a 765mL flask containing nitrogen gas at a temperature of 25.0°C and a pressure of 725 mmHg . The dry ice is allowed to sublime (convert from solid to gas) and the mixture is allowed to return to 25.0°C. What is the total pressure in the flask?

Answer 1

Answer : The total pressure in the flask is 1.86 atm.

Explanation :

First we have to calculate the pressure of $CO_2$ gas.

Using ideal gas equation :

$PV=nRT\\\\P_{CO_2}=\frac{w}{M}\frac{RT}{V}$

where,

P = Pressure of $CO_2$ gas = ?

V = Volume of $CO_2$ gas = 765 mL = 0.765 L     (1 L = 1000 mL)

n = number of moles

w = mass of $CO_2$ gas = 1.25 g

M = molar mass of $CO_2$ gas = 44 g/mol

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

T = Temperature of $CO_2$ gas = $25.0^oC=273+25.0=298K$

Putting values in above equation, we get:

$P_{CO_2}=\frac{w}{M}\frac{RT}{V}$

$P_{CO_2}=\frac{1.25g}{44g/mol}\frac{(0.0821L.atm/mol.K)\times 298K}{0.765L}=0.909atm$

Now we have to calculate the total pressure in the flask.

$P_T=P_{N_2}+P_{CO_2}$

Given :

$P_{CO_2}=0.909atm$

$P_{N_2}=725mmHg=\frac{725}{760}=0.954atm$

conversion used : (1 atm = 760 mmHg)

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

$P_T=0.954atm+0.909atm=1.86atm$

Therefore, the total pressure in the flask is 1.86 atm.