Question

The equilibrium constant for the reaction Cl2(g)=2Cl(g) at 2000K is 0.55atm. A sample of Cl2 is placed in a reaction bulb of volume 50.0mL, which is then heated to 2000K. The total pressure is found to be 1.36 atm. Calculate the mass of Cl2 originally placed in the bulb.

Answer 1

Solution:

               Cl₂ (g) <--> 2 Cl (g)

               Kp = 0.55 atm

               T = 2000 K

                Total pressure = 1.36 atm

                Volume = 50.0mL = 0.0050 mL

               

                 Now, total pressure of the system = pCl₂ + pCl = 1.36 atm    

                                                                                                           (I)                    

                 Also, Kp for the above reaction = pCl²/pCl₂ = 0.55 atm (II)

                pCl₂ = 1.36 atm – pCl                                                      (III)   

                Substituting (III) in (II), we get,

                             pCl²/(1.36 atm – pCl) = 0.55 atm

                             pCl² + 0.55pCl – 0.748 = 0

                  Solving the polynomial equation for pCl, we get,

                             pCl = 0.6325 atm

                  thus, pCl₂ = 1.36 – 0.6325 = 0.7274 atm

                  Now, assuming this as the ideal gas case, we can find number of moles of the Cl₂ added initially.

                            pV = nRT

                              n = pV/RT = 0.7274*0.050/0.0821*2000

                                  = 0.03637/164.2 = 2.21 * 10^-4 moles    

                     Now, n = mass of Cl₂ gas/ Molar mass of Cl₂ gas

                               Mass of Cl₂ gas = n * Molar mass of Cl₂ gas

                                                         = 2.21 * 10^-4 * 70.906

                                                         = 0.01570 g