If the equilibrium constant (Keq) equals 9.12x1012 for the following reaction between strontium and magnesium:
Sr(s) + Mg2+(aq)<==> Sr2+(aq) + Mg(s)
Calculate Eo for a strontium=magnesium battery.
To calculate the standard cell potential (Eo) for a strontium-magnesium battery, we will make use of the Nernst equation. The Nernst equation relates the standard cell potential to the reaction quotient (Q) and the equilibrium constant (Keq) for a given reaction.
The Nernst equation is given by:
E = Eo - (RT / nF) * ln(Q)
Where:
E is the cell potential under non-standard conditions,
Eo is the standard cell potential,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin,
n is the number of moles of electrons transferred in the balanced equation, and
F is the Faraday constant (96,485 C/mol).
In the given reaction, the balanced equation is:
Sr(s) + Mg2+(aq) ⇌ Sr2+(aq) + Mg(s)
We can see that 2 moles of electrons are transferred in this reaction since Mg2+ ion gains 2 electrons and Sr2+ ion loses 2 electrons.
Given: Keq = 9.12x10^12
At equilibrium, Q = Keq because the reaction has reached equilibrium. Thus, the Nernst equation becomes:
E = Eo - (RT / 2F) * ln(Keq)
Now, let's calculate Eo:
E = ?
Eo = E + (RT / 2F) * ln(Keq)
Since the values for R, T, and F are all constants, we can substitute their values into the equation:
Eo = E + (8.314 J/(mol·K) * T / (2 * 96,485 C/mol) * ln(Keq)
The temperature, T, is given in Kelvin. You can convert the temperature to Kelvin if it's given in Celsius by simply adding 273.15 to it.
After substituting the appropriate values and calculating the expression, you will obtain the value of Eo for the strontium-magnesium battery.