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Chapter 21: Q21.52P (page 975)

(a) How do the relative magnitudes of Q and K relate to the signs of 螖骋andEcell ? Explain.

(b) Can a cell do work when Q/K> 1or Q/K< 1? Explain.

Short Answer

Expert verified

a. The dependency of the sign of Ecell鈥夆�塧nd鈥夆�壩敵� is given below.

  • When, QK=1,鈥夆赌塃cell=0鈥夆�塧nd鈥夆�壩敵�=0
  • When, QK&濒迟;1,鈥夆赌夆赌塴苍QK<0. Therefore, Ecell>0鈥夆�夆�塧nd鈥夆�夆�壩敵�<0.Thus the reaction proceeds spontaneously.
  • When, QK&驳迟;1,鈥夆赌夆赌塴苍QK>0. Therefore,Ecell<0鈥夆�夆�塧nd鈥夆�夆�壩敵�>0. Thus the reaction proceeds non- spontaneously.

b. A cell is spontaneous when QK is less than 1.

Step by step solution

01

Sign of   Ecell  and  ΔG

When a redox reaction in a cell is in equilibrium under standard conditions, the equilibrium constant is denoted by K. The equilibrium constant under non-standard conditions is denoted by Q.

The Nernst equation is given below.

Ecell=Ecello-RTnF濒苍蚕鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(1)

We also know,

E0cell鈥�=鈥夆赌�RTnF濒苍碍鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(2)

Substituting the value of E0cell in equation (1), we get:

role="math" localid="1659591790741" Ecell=鈥夆赌夆赌�RTnF濒苍碍鈥夆赌�-RTnF濒苍蚕鈥夆赌夆赌夆赌夆赌夆赌夆赌�=-RTnFlnQK鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(3)

Now, we will see three conditions for predicting the signs for Ecell鈥夆�塧nd鈥夆�壩敵�.

  • When, QK=1,鈥夆赌塃cell=0鈥夆�塧nd鈥夆�壩敵�=0
  • When, QK&濒迟;1,鈥夆赌夆赌塴苍QK<0. Therefore,Ecell>0鈥夆�夆�塧nd鈥夆�夆�壩敵�<0.Thus the reaction proceeds spontaneously.
  • When, QK&驳迟;1,鈥夆赌夆赌塴苍QK>0. Therefore, Ecell<0鈥夆�夆�塧nd鈥夆�夆�壩敵�>0.Thus the reaction proceeds non- spontaneously.
02

Spontaneity of the cell

When QK&濒迟;1,鈥夆赌夆赌塴苍QK<0.

Consequently, Ecell>0鈥夆�夆�塧nd鈥夆�夆�壩敵�<0. Thus, a cell is spontaneous when QKis less than 1.

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