Pt(s) | H2(g, 2.0 bar) | H+ (pH = 3.0) || Cl -(aq, 0.85 mol·L-1)) | Hg2Cl2(s) | Hg(l)

I need to calculate the voltage for the cell.

I have used 1E-3 M for my concentration of H+ given the pH=3 . I don't know how to incorporate the 2.0 bar into the nernst equation. I keep coming up with -.1833 V but that is incorrect.

The bar goes in for partial pressure of H2 gas so if we have

H2 ==> 2H^+ + 2e then

E = Eo - (0.059/2)*log [(H^+)^2/pH2]
I'm unclear if the bar has become the standard of if your prof is using 1 atm for the standard. The difference
a. if bar is standard, you simply substitute 2 for partial pressur.
b. if atm is standard, you convert 2 bar to atm.
c. In any even, the difference between bar and atm is small. 1 bar = 0.9869 atm.

To calculate the voltage for the cell using the Nernst equation, you first need to write the balanced redox reaction for the cell. Looking at the given cell notation:

Pt(s) | H2(g, 2.0 bar) | H+ (pH = 3.0) || Cl-(aq, 0.85 mol·L-1)) | Hg2Cl2(s) | Hg(l)

The balanced redox reaction can be written as:

H2(g) + 2 H+ (aq) + 2 Cl-(aq) → 2 HCl(aq)

Now, you can construct the Nernst equation which relates the cell potential (E) to the concentrations of the reactants and products:

E = E° - (RT / (nF)) ln(Q)

Where:
- E is the cell potential (voltage)
- E° is the standard cell potential (which you need to look up for the given reaction)
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
- n is the number of electrons transferred in the balanced redox reaction (in this case, n = 2 since 2 H+ ions are involved in the reaction)
- F is the Faraday constant (96,485 C/mol)
- Q is the reaction quotient, which can be calculated using the concentrations of reactants and products.

To incorporate the 2.0 bar pressure of H2 into the Nernst equation, you need to convert it to concentration. The concentration of H2 can be calculated using the ideal gas law:

PV = nRT

Rearranging the equation:

n/V = P/RT

Since you have the pressure (2.0 bar) and the ideal gas constant (R), you can calculate the molar concentration of H2.

Now, let's put everything together. First, convert the pressure of H2 to concentration using the ideal gas law:

n/V = P/RT
n/V = (2.0 bar) / (0.08314 bar·L·mol^(-1)·K^(-1) × T(K))

Assuming the temperature is given, substitute the values and solve for n/V (the concentration of H2 in mol·L-1).

Once you have the concentration of H2, use it along with the concentration of H+ and Cl- (given in the problem) in the Nernst equation:

E = E° - (RT / (nF)) ln(Q)

Where Q is the reaction quotient and can be calculated as:

Q = [HCl(aq)]^2 / [H+ (aq)]^2 [Cl- (aq)]

Substitute the concentrations into the equation and calculate ln(Q). Then, substitute E° (which can be looked up) together with the other known values into the equation and solve for E.

Be sure to carefully double-check your calculations and units to avoid any errors.