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Assertion A: In equation Ī r G = ā n F E c e l l , \Delta_r G = - nF E_{cell}, Ī r ā G = ā n F E ce ll ā , value of Ī r G \Delta_r G Ī r ā G depends on n. \\ Reason R: E c e l l E_{cell} E ce ll ā is an intensive property and Ī r G \Delta_r G Ī r ā G is an extensive property.
medium
Thermodynamics
2023
chemistry
Both A and R are true and R is the correct explanation of A.
Both A and R are true and R is NOT the correct explanation of A.
A is true but R is false.
A is false but R is true.
Explanation To solve this problem, we need to analyze the given assertion and reason. \\
Assertion A: In the equation Ī r G = ā n F E c e l l , \Delta_r G = - nF E_{cell}, Ī r ā G = ā n F E ce ll ā , the value of Ī r G \Delta_r G Ī r ā G
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depends on
Reason R:
is an intensive property and
is an extensive property.
Let's break down each part:
ā¢ The equation
Ī r G = ā n F E c e l l \Delta_r G = - nF E_{cell} Ī r ā G = ā n F E ce ll ā is used to relate the Gibbs free energy change
Ī r G \Delta_r G \\
Ī r ā G to the cell potential
E c e l l . E_{cell}. \\
E ce ll ā . ā¢ Here,
is the number of moles of electrons transferred in the reaction,
is Faraday's constant,
and
is the electromotive force (emf) of the cell.
ā¢
is an extensive property, meaning it depends on the amount of substance involved.
ā¢
is an intensive property, meaning it does not depend on the amount of substance.
Analyzing the assertion:
ā¢ Since
is calculated using
(the number of moles of electrons), it is directly proportional to
ā¢ Therefore, the assertion that
depends on
is true.
Analyzing the reason:
ā¢
being an intensive property means it remains constant regardless of the system size.
ā¢
being an extensive property means it scales with the size of the system or the amount of substance.
ā¢ The reason correctly states the nature of these properties.
Conclusion:
ā¢ Both the assertion and the reason are true.
ā¢ The reason correctly explains why
depends on
because
affects the extensive property
Ī r G . \Delta_r G. \\
Ī r ā G . Therefore, the correct option is 1: Both A and R are true and R is the correct explanation of A.