Nonideal Gas Part A A typical gas molecule is about 20 1010m

Nonideal Gas

Part A

A typical gas molecule is about 2.0 ×1010m in radius. A gas would begin to exhibit behaviors deviating significantly from ideal-gas behavior when its volume per molecule approaches the volume of an individual molecule. At an ordinary temperature of 300K, estimate the pressure that this would require. Express your answer using one significant figure.

Express your answer using one significant figure.

The answer is not 1.24 x 10^8

Solution

from ideal gas Law, we have

         PV = nRT

So, the required pressure is,

      P = nRT/V

here, V = (4/3)*pi*r^3*6.022*10^23

therefore,

          P = 1*8.314*300/((4/3)*pi*r^3*6.022*10^23)

             = 1*8.314*300/((4/3)*pi*(2*10^-10)^3*6.022*10^23)

            = 1.24*10^8 Pa

            = 1x10^8 Pa        [ONE SIGNIFICANT FIGURE]