± Enthalpy, Entropy, and Spontaneity The spontaneity of a reaction depends both

Question

± Enthalpy, Entropy, and Spontaneity The spontaneity of a reaction depends both on the enthalpy change, ,H, and entropy change, ,S Reactions that release energy produce more stable products, and the universe tends toward disorder Thus, an exothermic reaction with a positive entropy change will always be spontaneous. Mathematically this relationship can be represented as where ,G is the change in Gibbs energy and T K is the Kelvin temperature. If .G is negative then the reaction is spontaneous. If ArG is positive then the reaction is nonspontaneous as written but spontaneous in the reverse direction.

Explanation / Answer

we know that

for a reaction to be spotaneous

dG < 0

now

the relation between dG, dH and dS is given by

dG = dH - TdS

now

dG < 0

dH - TdS < 0

given

dH = -70 x 1000 J/mol = -70000 J/mol

dS = -0.2 x 1000 J/mol = -200 J/mol

now

dH - TdS < 0

-70000 - ( T x -200) < 0

200T - 70000 < 0

200T < 70000

T < 350

so

the reaction is spontaneous below 350 K

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