Can someone please help me with this problem. The following cell is set up to measure the concentration of K^+ in blood serum
Ag,AgCl | KCl(aq), c=1mol/L | K^+ selective membrane | KCl, c mol/L in serum || NaCl(aq), c=1mol/L | AgCl,Ag
1) If the cell potential difference is +0.148V and the temperatsure 25 degrees, use Nerst equation to calculate an estimate of the K^+ concentration in the serum
Any help would be greatly appreciated
To calculate the estimated K+ concentration in the serum, you can use the Nernst equation. The Nernst equation relates the cell potential difference to the concentration of the ion of interest. In this case, the equation becomes:
E = E° - (RT/nF) * ln([K+]out / [K+]in)
Where:
E is the cell potential difference (+0.148V in this case)
E° is the standard cell potential (which we will assume to be 0V for simplicity)
R is the ideal gas constant (8.314 J/(mol*K))
T is the temperature in Kelvin (25 + 273 = 298K)
n is the number of moles of electrons transferred (1 for this cell setup)
F is the Faraday constant (96,485 C/mol)
[K+]out is the concentration of K+ in the outer compartment (KCl, c mol/L in serum)
[K+]in is the concentration of K+ in the inner compartment (KCl(aq), c=1 mol/L)
To solve for [K+]out, we rearrange the equation as:
ln([K+]out / 1) = (0.148V / (8.314 J/(mol*K)) * 298K) / (1 * 96,485 C/mol)
Now we can solve this equation for [K+]out using natural logarithm properties.