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the molar entropies of carbon monoxide and carbon dioxide at 25C are 197.7 and 213.8 J/Mol*k...

the molar entropies of carbon monoxide and carbon dioxide at 25C are 197.7 and 213.8 J/Mol*k respectively. How many times more accessible microstates does CO2 have than CO at 25C

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Answer #1

The molar entropy in terms of micro-state is given as :

S=K​​​​​B​​​​​*lnΩ

S=entropy

K​​​​​​B=Boltzmann Constant=1.38*10-23J/K

Ω=number of microstates

Given,

Molar entropy of CO = 197.7 J/molK

Molar entropy of CO2 = 213.8 J/molK

Suppose for 1 mole of CO and CO2, then the entropy will be :

S(CO) = 197.7 J/molK × 1 mol

S(CO) = 197.7 J/K

S(CO2) = 213.8 J/molK × 1 mol

S(CO2) = 213.8 J/K

ln Ω(CO)=S(CO)÷KB

ln Ω(CO2)=S(CO2)÷KB

Dividing these two equations we get,

ln Ω(CO2)÷ln Ω(CO)=S(CO2)÷S(CO)

ln Ω(CO2)÷ln Ω(CO)=213.8÷197.7=1.08

ln Ω(CO2)=1.08*ln Ω(CO)

So 1.08 times more

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