1.Using Nerst, find the E of the cell for the dicromate redox system:

A.under standard conditions.

B.under neutral solutions instead of acid solutions.

2.Use Nerst and the hydrogen half equation to obtain an expression for pH.

1. To find the cell potential (E) using the Nernst equation for the dichromate redox system, we need to know the half-reactions involved and the corresponding standard potential (E°) values. The dichromate redox system can be represented by the following half-reactions:

Cr2O7^2-(aq) + 14H+(aq) + 6e- → 2Cr^3+(aq) + 7H2O(l)
2H+(aq) + 2e- → H2(g)

A. Under standard conditions:
Under standard conditions, the concentrations of all species involved are at 1 M concentration, and the temperature is 298 K (25 °C). The Nernst equation becomes:

E = E° - (RT/nF) ln(Q)

Where E° is the standard cell potential (found in tables), R is the gas constant (8.314 J/(mol K)), T is the temperature in Kelvin, n is the number of electrons transferred in the balanced equation, F is Faraday's constant (96,485 C/mol), and Q is the reaction quotient.

For the dichromate redox system in acid solution:
E° = E°(Cr3+/Cr2O7^2-) + E°(H+/H2)
= 1.33 V + 0.00 V
= 1.33 V

Substituting the values into the Nernst equation and simplifying, we get:
E = 1.33 V - (8.314 J/(mol K) * 298 K)/(6 * 96485 C) * ln(Q)

B. Under neutral solutions instead of acid solutions:
To find the E value under neutral conditions, we need the half-reaction involving H+ in neutral solution. In neutral media, the half-reaction involving H+ is different. It can be represented as:

2H2O(l) + 2e- → H2(g) + 2OH-(aq)

Using this half-reaction, the standard potential (E°) of the system changes. We need to find the updated E° value for the dichromate redox system in neutral solution and then follow the same Nernst equation as in part A to calculate E.

2. To obtain an expression for pH using the Nernst equation and the hydrogen half-reaction, we need to consider the formula for the Nernst equation:

E = E° - (RT/nF) ln(Q)

For the hydrogen half-reaction in acidic solution:
2H+(aq) + 2e- → H2(g)

The Nernst equation can be rearranged to solve for the pH:

E = E° - (RT/2F) ln(H+)^2

Since pH is defined as the negative logarithm of the hydrogen ion concentration (pH = -log[H+]), we can rewrite the equation as:

E = E° - (RT/2F) ln(10^-pH)^2

Simplifying further, we get the expression for pH:

pH = -((E - E°) * 2F / RT)

This equation allows us to calculate the pH of a solution using the measured cell potential (E) and the standard potential (E°) for the hydrogen half-reaction.