express the answer on L

Question

A piece of dry ice (solid carbon dioxide) with a mass of 31.5 g is allowed to sublime (convert from solid to gas) into a large balloon.

Assuming that all of the carbon dioxide ends up in the balloon, what is the balloon's volume at 23 °C and a pressure of 756 mmHg?

Answer 1

Hi Made!

 

I think this is a job for the ideal gas law (presuming we can treat the sublimated carbon dioxide as an ideal gas, which we usually can for most gases).  That, as you may know, is (in perhaps its most common form):

 

PV = nRT  

 

where 

 

P = pressure

V = volume

n = number of moles

R = ideal gas constant

T = temperature

 

I am going to use a common value for R of 8.314 J/mol/K.  To make the units work, my pressure then needs to be in pascals (Pa), and my volume will come out in m³, which I can then convert to liters.  And temperature has to be in kelvin.  So I have some conversion to do.

 

NOTE:  You could also choose a different value for R that has units that would make it so you didn't have to convert; that is up to you.  You would just have to look up (if you did not already know) the correct value for R in those units.

 

756 mmHg * (1.01x10⁵ Pa)/(760 mmHg) = 1.00 x 10⁵ Pa

23 °C = 23+273.16 K = 296.16 K

 

And now, the last input we need:  n, the number of moles.  How many moles are in 31.5 g of carbon dioxide?  Well, each molecule has 1 carbon atom (12 g/mol) and two oxygen atoms (16*2 = 32 g/mol).  So 1 mol of CO₂ = 12+32 = 44 g/mol  (actually 44.0095, to account for the multiple isotopes of both atoms, but I am going to use 44 g/mol).

 

So  31.5 g * 1 mol/44 g = 0.716 mol = n

 

Now, I can populate the ideal gas law and solve for V (in m³, which I can then convert to L)

 

(1.00x10⁵ Pa)(V) = (0.716 mol)(8.314 J/mol/K)(296.16 K)

 

Solve this expression for V in m³, then convert to L, and that is the answer.

 

If you would like to check am answer, or if you have any questions about the setup, please let me know.  Hope this helps!