2. 65 moles of an ideal gas at 36. 9oC and 40,205Pa occupy 54. 7mL. Additional gas is added to this container such that the temperature and pressure change to 113. 7oC and 131,874Pa, with the volume remaining the same. How many moles of this gas were added?



Answer :

3.64 moles of this gas were added.

The ideal gas law shows the relationship between pressure,volume,number of moles and temperature in an ideal gas. It is used to predict the behaviour of real gases under similar conditions.  

            PV=n RT

         P=pressure

         V=volume (L)

         n= number of moles (mole)

        R= universal gas constant (8.31J/K mol)

         T= temperature (K)

 So, the expression becomes,

        P1 . V1 /N1 .T1 = P2 .V2 /N2 .T2   as R is constant.

Here,2.65 moles of an ideal gas at 36.9C and 40,205Pa occupy 54.7L and the temperature and pressure change to 113.7C and  131,874Pa.

             

  Substituting all values in the expression,

               N2 = (P2 .n1.T1)  / (P1 .T2 )   as  volume remains the same.

                   =( 131,874Pa . 2.65 mol . 36.9C)  /( 40,205Pa  . 113.7C)

              = 3.64  moles

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