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Question

Find Kp for t following reaction 
  SO2 Cl2 gives SO2 +Cl2
If sulphuryl chloride decomposes to the extent of 91.2% a t 102°C and total pressure 1 atm


Solution

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At 25°C, gaseous SO2Cl2 decomposes to SO2(g) and Cl2(g) to the extent that 12.5% of the original SO2Cl2 (by moles) has decomposed to reach equilibrium. The total pressure (at equilibrium) is 0.900 atm. Calculate the value of Kp for this system.

Initially 

mol SO2Cl2 = x 
mol SO2 and mol Cl2 = 0 

12.5%x mol SO2Cl2 decomposes to form 12.5%x mol SO2 and 12.5%x mol Cl2 

At equilibrium 

mol SO2Cl2 = x - 12.5%x = 87.5%x 
mol Cl2 = 12.5%x 
mol SO2 = 12.5%x 

Kp = P(SO2) . P(Cl2) / P(SO2Cl2) 

total mol gases at equil. = (87.5%x)+(12.5%x)+(12.5%x)=112.5%x 

P(SO2) = 12.5%x / 112.5%x * 0.9 = 0.1 
P(Cl2) = 12.5%x / 112.5%x * 0.9 = 0.1 
P(SO2Cl2) = 87.5%x / 112.5%x * 0.9 = 0.864 

Therefore Kp = 0.1^2 / 0.864 = 0.01157 atm

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