Given the values of ? H ?rxn, ? S ?rxn, and T below, determine ? S univ. Also, p

Question

Given the values of ?H?rxn, ?S?rxn, and Tbelow, determine ?Suniv. Also, predict whether each reaction will be spontaneous or nonspontaneous

A)?H?rxn= 86kJ , ?Srxn= 142J/K , T= 308K

Express your answer using two significant figures.

B)?H?rxn= 86kJ , ?Srxn= 142J/K , T= 762K

Express your answer using one significant figure.

C)?H?rxn= 86kJ , ?Srxn=? 142J/K , T= 308K

Express your answer using one significant figure.

D)?H?rxn=? 86kJ , ?Srxn= 142J/K , T= 404K

Express your answer using one significant figure.

Explanation / Answer

A.Given DeltaH(rxn) = 86KJ, DeltaS(rxn) = 142J/K = 142Jx(1kJ/1000J)/K = 0.142kJ/K

T = 308K.

Now DeltaG(rxn) can be calculated as

DeltaG(rxn) =  DeltaH(rxn) - TxDeltaS(rxn) = 86KJ - 308Kx(0.142kJ/K) = +42.26 KJ

For a reaction to be spontaneous, DeltaG(rxn) should be negative. Since DeltaG(rxn) for the above reaction is positive, hence the reaction is nonspontaneous.

Now DeltaS(universe) can be calculated as

DeltaG(rxn) = - TxDeltaS(universe)

=> DeltaS(universe) = - DeltaG(rxn) / T = - (+42.26 KJ) / 308K = - 0.137kJ/K = -140J/K (upto 2 SF, answer)

B: Given DeltaH(rxn) = 86KJ, DeltaS(rxn) = 142J/K = 142Jx(1kJ/1000J)/K = 0.142kJ/K

T = 762K.

Now DeltaG(rxn) can be calculated as

DeltaG(rxn) =  DeltaH(rxn) - TxDeltaS(rxn) = 86KJ - 762Kx(0.142kJ/K) = - 22.2 KJ

For a reaction to be spontaneous, DeltaG(rxn) should be negative. Since DeltaG(rxn) for the above reaction is negative, hence the reaction is spontaneous.

Now DeltaS(universe) can be calculated as

DeltaG(rxn) = - TxDeltaS(universe)

=> DeltaS(universe) = - DeltaG(rxn) / T = - ( - 22.2 KJ) / 762K = + 0.029kJ/K = +30J/K (upto 1 SF, answer)

C. This is same as A, and the only difference is that here we need to find the answer in 1 SF.

Given DeltaH(rxn) = 86KJ, DeltaS(rxn) = 142J/K = 142Jx(1kJ/1000J)/K = 0.142kJ/K

T = 308K.

Now DeltaG(rxn) can be calculated as

DeltaG(rxn) =  DeltaH(rxn) - TxDeltaS(rxn) = 86KJ - 308Kx(0.142kJ/K) = +42.26 KJ

For a reaction to be spontaneous, DeltaG(rxn) should be negative. Since DeltaG(rxn) for the above reaction is positive, hence the reaction is nonspontaneous.

Now DeltaS(universe) can be calculated as

DeltaG(rxn) = - TxDeltaS(universe)

=> DeltaS(universe) = - DeltaG(rxn) / T = - (+42.26 KJ) / 308K = - 0.137kJ/K = -100J/K (upto 1 SF, answer)

D.Given DeltaH(rxn) = 86KJ, DeltaS(rxn) = 142J/K = 142Jx(1kJ/1000J)/K = 0.142kJ/K

T = 404K.

Now DeltaG(rxn) can be calculated as

DeltaG(rxn) =  DeltaH(rxn) - TxDeltaS(rxn) = 86KJ - 404Kx(0.142kJ/K) = +28.63 KJ

For a reaction to be spontaneous, DeltaG(rxn) should be negative. Since DeltaG(rxn) for the above reaction is positive, hence the reaction is nonspontaneous.

Now DeltaS(universe) can be calculated as

DeltaG(rxn) = - TxDeltaS(universe)

=> DeltaS(universe) = - DeltaG(rxn) / T = - (+28.63 KJ) / 404K = - 0.070kJ/K = -70J/K (upto 1 SF, answer)

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