Nitrogen dioxide, NO2, dimerizes easily to form dinitrogen tetroxide , N2O4 :

2NO2<===>N2O4
a) Calculate Change in reaction G* and K for this equilibrium.
b) Calculate the (e) (the measure of the progress of the reaction) for this equilibrium if 1.00 mol NO2 were present initially and allowed to come to equilibrium with the dimer in a 20.0 l system?

delta Gorxn = (n*DGoproducts)-(DGoreactants), then

delta Go = -RT*lnKp.
I would then convert this to Kc by
Kp = Kc(RT)delta n

I don't know what you mean by (e).
.............2NO2 ==> N2O4
initial......1 mol.....0
change......-2x........x
equil........1-2x.......x

Kc = (N2O4)/(NO2)^2
Don' forget to convert mole to M by moles/L and that is a 20.0 L container.

a) To calculate the change in standard Gibbs free energy (∆G°) and equilibrium constant (K) for this equilibrium, we need to use the equation:

∆G° = -RT * ln(K)

Where:
R = gas constant (8.314 J/mol·K)
T = temperature in Kelvin (usually given)

To find the change in standard Gibbs free energy, we need to know the temperature at which the reaction is taking place.

b) To calculate the measure of progress of the reaction (e), we first need to determine the initial concentration of NO2 and the concentration of N2O4 at equilibrium.

Let x be the change in concentration of NO2 (in mol) as the reaction progresses.

Initially, the concentration of NO2 is 1.00 mol in a 20.0 L system, so the initial concentration of NO2 is [NO2] = 1.00 mol/20.0 L = 0.0500 mol/L.

At equilibrium, the concentration of NO2 will be (0.0500 - x) mol/L, and the concentration of N2O4 will be (x/20.0) mol/L due to the stoichiometry of the balanced equation.

To find the value of x and calculate e:

1. Set up the expression for the equilibrium constant (K):

K = [N2O4] / [NO2]^2
K = (x/20.0) / [(0.0500 - x)^2]

2. Rearrange and solve for x:
(x/20.0) = K * [(0.0500 - x)^2]
x/20.0 = K * (0.0025 - 0.05x + x^2)
x = 20.0K * (0.0025 - 0.05x + x^2)

This is a quadratic equation, which can be solved using the quadratic formula. Once x is determined, e can be calculated by dividing x by the initial concentration of NO2.

Please provide the temperature of the reaction so that we can proceed with the calculations.

To calculate the change in standard free energy (∆G°) and equilibrium constant (K) for this equilibrium reaction, we need to know the standard free energy of formation (∆G°f) for each compound involved.

A) Calculating the ∆G°:
The standard free energy change for a reaction (∆G°) can be calculated using the equation:

∆G° = Σ∆G°f (products) - Σ∆G°f (reactants)

The ∆G°f values for NO2 and N2O4 can be found in a table of standard thermodynamic data. Let's assume that:
∆G°f(NO2) = x kJ/mol
∆G°f(N2O4) = y kJ/mol

Therefore, the equation becomes:
∆G° = 2 * ∆G°f(N2O4) - 2 * ∆G°f(NO2)

Substituting the values, we get:
∆G° = 2y - 2x

B) Calculating the equilibrium constant (K):
The equilibrium constant (K) for a reaction can be calculated using the equation:

K = e^(-∆G° / (RT))

Where:
- ∆G° is the change in standard free energy calculated above
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin

C) Calculating the measure of progress (e):
To calculate the measure of progress (e) for this equilibrium, we need to use the given initial amount of NO2 and the stoichiometry of the balanced equation.

From the balanced equation:
2 mol NO2 <===> 1 mol N2O4

Since 1.00 mol NO2 was initially present, according to the balanced equation, we have:
1.00 mol NO2 <===> 0.50 mol N2O4

Now, we can use the ideal gas law equations to find the concentration of NO2 and N2O4 in the 20.0 L system. The concentration is given by the formula:

c = n/V

Where:
- c is the concentration in mol/L
- n is the number of moles
- V is the volume in liters

Given values:
- Initial moles of NO2 = 1.00 mol
- Volume of the system (V) = 20.0 L

From these values, we can find the initial concentration of NO2 and N2O4.

Now, using the initial concentrations and the balanced equation, we can calculate the value of e.

Hence, to answer the questions, we need the actual values of ∆G°f(NO2), ∆G°f(N2O4), and the temperature (T) to complete the calculations.