what is the volume in cubic meter and in cubic decimeter of 2.0mol of nitrogen on gas at 1000c and 100,000pa? (R=8.31j/molk)

Given parameters:

Number of moles of Nitrogen = 2.0mole

Temperature of the gas = 1000c

Pressure on the gas = 100000Pa

Gas constant R = 8.31J/molK = 0.082atmdm³mol⁻¹k⁻¹

Unknown:

Volume in cubic meter and cubic decimeter = ?

Solution:

The ideal gas law is given as;

       PV  = nRT

where P is the pressure on the gas

          V is the volume of the gas

         n is the number of moles

         R is the gas constant

         T is the temperature of the gas

Let us convert to appropriate units;

      1000°C to K;

       K  = 1000 + 273  = 1273K

100000Pa to atm;

           101325Pa  = 1atm

           100000Pa = 0.99atm

 Input the parameters and solve for the unknown;

      0.99 x V  = 2 x 0.082 x 1273

                   V  = 210.9dm³

to m³;

        1000dm³   = 1m³

        210.9dm³ =   = 0.21m³

here we have to get the change of moles on decrease the volume of the reaction in gas phase.

the   per the given options it will decrease by (d) 11-50%

we know, on decreasing the volume of the gas phase reaction the reaction moves to the product side.

the reaction:                     so₂cl₂ (g) = so₂ (g) + cl₂ (g)         total

the moles at equilibrium:   1 - α                 α               α           = 1+α

concentrations:                   1 - α               α               α           = 1 + α

(concentration = moles/volume, as volume is 1 l)

(where α is the degree of dissociation)

now the dissociation constant in terms of concentration is :

=  

or,

or,   = (at v = 1l)

the reaction:                     so₂cl₂ (g) = so₂ (g) + cl₂ (g)         total

the moles at equilibrium:   1 - α                 α               α           = 1+α

concentrations:               (1 - α)/0.5           α/0.5         α/0.5       = (1 + α)/0.5

thus, the dissociation constant in terms of concentration is :

or,  

=  

so, the change of 1 : 1/0.5

or, 1: 2

thus it will decrease by 50%.

or, as per the given options it will decrease by 11-50%