In an ultrahigh vacuum system, the pressure is measured to be 8.4 × 10−11 torr (where 1 torr = 133 Pa). The gas molecules have a molecular diameter of 2.2 × 10−10 m and the temperature is 310 K. Avogadro's number is 6.02214×1023 1/mol. Find the number of molecules in a volume of 0.87 m3 . Answer in units of molecules.

The number of molecules in the volume is   molecules

Explanation:

From the question we are told that

    The pressure of the ultrahigh vacuum is

     The molecular diameter of the gas molecules

      The temperature is  

      Avogadro's number is

        The volume of the gas is

From the ideal gas law[] that the number of mole is mathematically represented as

Where R is the gas constant with a value  

  Substituting values

The number of molecules is mathematically represented as

  Substituting values

              molecules