For the electrochemical cell Ca(s) + Ca2+(aq, 1​M)∥Cu2+(aq, 1​M)  ∣  Cu(s) The standard emf of the cell is 3.20 V at 300 K. When the concentration of Ca2+ is changed to x M, the cell potential changes to 3.185 V at 300 K. The value of 100x is__________.[Given:  FR  =  11500​KV−1, where F is the Faraday constant and R is the gas constant,  ℓn​3.15  =  1.15]

To find the value of 100x, we can use the Nernst equation, which relates the cell potential to the concentrations of the species involved. The Nernst equation is given by:

E = E° - (RT/nF) * ln(Q)

Where: E is the cell potential E° is the standard cell potential R is the gas constant T is the temperature in Kelvin n is the number of electrons transferred in the balanced equation F is the Faraday constant Q is the reaction quotient

In this case, the balanced equation for the cell is:

Ca(s) + Ca2+(aq) → Cu2+(aq) + Cu(s)

The number of electrons transferred in this reaction is 2.

Given that the standard cell potential (E°) is 3.20 V at 300 K, we can substitute these values into the Nernst equation:

3.20 V = E° - (RT/2F) * ln(Q)

Now, let's consider the new concentration of Ca2+ as x M. The reaction quotient (Q) can be calculated using the concentrations of the species involved:

Q = [Cu2+(aq)] / [Ca2+(aq)]

Since the concentration of Cu2+(aq) is 1 M, and the concentration of Ca2+(aq) is x M, we have:

Q = 1 / x

Substituting this value into the Nernst equation, we get:

3.185 V = 3.20 V - (RT/2F) * ln(1/x)

Simplifying the equation, we have:

0.015 V = (RT/2F) * ln(x)

Now, we can substitute the given values into the equation. The value of R is the gas constant, which is approximately 8.314 J/(mol·K). The value of F is the Faraday constant, which is given as 11500 K^-1.

0.015 V = (8.314 J/(mol·K) * 300 K / (2 * 11500 K^-1)) * ln(x)

Simplifying further:

0.015 V = (0.036 J/mol) * ln(x)

To find the value of 100x, we need to solve for x. Rearranging the equation:

ln(x) = (0.015 V) / (0.036 J/mol)

Using the given value that ln(3.15) = 1.15, we can substitute this into the equation:

ln(x) = 1.15

Now, we can solve for x by taking the exponential of both sides:

x = e^1.15

Finally, we can calculate the value of 100x:

100x = 100 * e^1.15

Calculating this value, we find:

100x ≈ 316.227

Therefore, the value of 100x is approximately 316.227.