To determine the value of
X from the galvanic cell reaction and the emf values provided, the Nernst equation is employed. The standard emf
(E0) and the non-standard condition emf
(E) of the cell are related by the Nernst equation, which incorporates the concentration of the ionic species involved:
The general form of the Nernst equation is:
E=E0−‌‌ln‌Qwhere:
E is the cell potential under non-standard conditions.
E0 is the standard cell potential.
R is the universal gas constant
(8.314J/‌mol⋅K).
T is the temperature in Kelvin.
n is the number of moles of electrons transferred in the electrochemical reaction.
F is the Faraday constant
(96485C/‌mol).
Q is the reaction quotient at non-standard conditions.
Let's rearrange the Nernst equation to find
n :
Let's rearrange the Nernst equation to find
n :
n=‌Given data:
‌E0=2.71V‌E=2.651VTemperature (
T ) can effectively be assumed at
298K(25∘C), standard laboratory condition if not specified.
The reaction given is:
A( s)+B2+(1⋅10−XM)⟶B( s)+A2+(0.1M)‌. ‌Q, the reaction quotient, can be calculated as:
Q=‌=‌=10X−1.If we apply the approximation due to the small difference in emf and convert
ln to
log base-10, the Nernst equation in practical terms is:
‌2.71−2.651=‌‌log(10X−1)‌0.059=‌(X−1),Solve for
n,
n=X−1 And since the number of electrons
(n ) involved in this redox reaction dictates the change on the ions which is 2 for both
A2+ and
B2+, thus
n=2. Therefore,
‌2=X−1‌X=3Hence, the value of
X is 3 , so the correct option is:
Option C:
X=3.