10 m3 of carbon dioxide is originally at a temperature of 50 °c and pressure of 10 kpa. determine the new density and volume of the carbon dioxide if the temperature and pressure change to 75 oc and 15 kpa.

Answer : The new density and new volume of carbon dioxide gas is 0.2281 g/L and respectively.

Explanation :

First we have to calculate the new or final volume of carbon dioxide gas.

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

where,

= initial pressure of gas = 10 kPa

= final pressure of gas = 15 kPa

= initial volume of gas =

= final volume of gas = ?

= initial temperature of gas =

= final temperature of gas =

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

The new volume of carbon dioxide gas is

Now we have to calculate the new density of carbon dioxide gas.

Formula for new density will be:

where,

= new pressure of gas = 15 kPa

= new temperature of gas =

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

R = gas constant = 8.314 L.kPa/mol.K

= new density

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

The new density of carbon dioxide gas is 0.2281 g/L