An inflated balloon contains X air molecules. After some time the volume of the balloon is found to be the half at the same temperature and pressure when a few air molecules are expelled out. a)How many molecules will be there in the balloon now? b) Which is the gas law associated with this?

(a): The balloon will contain number of molecules now.

(b): The gas law associated with this is Avogadro's law.

Explanation:

Avogadro's law states that the volume of the gas is directly proportional to the number of moles of the gas at constant pressure and temperature

Mathematically,

                  (At constant pressure and temperature)

OR

              .....(1)

where,

= Initial volume and number of moles

= Final volume and number of moles

We are given:

Putting values in equation 1, we get:

(a):

If number of moles of gas contains X number of molecules

So, number of moles of gas will contain = number of molecules

Hence, the balloon will contain number of molecules now.

(b): The law used is Avogadro's law.

the grams   of   barium that   are in   2.3 x 10^23   atoms of barium   is   52.4 g (answer c)

    calculation

mass = moles   of ba   x molar   mass of ba

  molar mass of ba from periodic table=   137.3 g/mol

  use the   avogadro's law   constant   to   calculate the moles of barium

  that   is     1 mole =   6.02   x 10^23 atoms

                    ? moles = 2.3 x 10^23   atoms

by cross   multiplication

=(1 mole   x 2.3x 10^23 atoms)   / 6.02   x10^23 atoms)=   0.382   moles

mass   is therefore = 137.3   g/mol x 0.382 mol = 52.4 ( answer c)

explanation: