density = P/MRT = (1.00 atm) / ((28.97 g/mol) * (0.08206 L*atm /Kmol)*(277.6 K))

Question

density = P/MRT = (1.00 atm) / ((28.97 g/mol) * (0.08206 L*atm /Kmol)*(277.6 K)) = 0.00152 g/cm^3

Assume that the above equation and solution are correct. You must help me resolve BOTH of the following two issues and help me understand why things are the way they are to get points:

ISSUE 1: I am having a hard time with the units of the solution.  No matter what I do to cancel out units the closest thing I get to g/cm^3 is (mol*mol)/g*L. What am I doing wrong and how do I fix it?

ISSUE 2: Furthermore, while the numbers check out in that 1/(28.97 * 0.08206*277.7) = 0.00152, we were dealing with liters, not cm^3. When liters is converted to cm^3 we divide by 1000, right? So wouldn't our answer be 1.52 *10^(-6) g/cm^3 instead of 0.00152 g/cm^3? Why isn't this the case?

Explanation / Answer

PV = nRT where n = number of moles = mass/mola mass = m/M

PV = ( m RT/M)

(m/V) = PM/RT   

denisty = m/V =(PM / RT) where P = pressure in atm , M = mol wt in gm /mol , T = temp in K , R = 0.0821 atm liter/ kelvin

now we get denisty in units of ( atm x gm mol^-1) / ( atm liter kelvin^-1 x kelvin ) = gm/liter

1 liter = 1000 cubic centimeters hence

units of density can also be in gm/cc

now density = ( 1 x 28.97 )/( 0.08206 x 277.6) = 1.272 gm/liter

density in gm/cc = 1.272 /1000cc = 0.00127 gm/cc

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