calculate the equilibrium constants at 25°C for each reaction. ΔGf° for BrCl(g) is −1.0 kJ/mol

Br2(g) + Cl2(g) 2 BrCl(g)

dGrxn = (n*dG products)-(n*dG reactants)

Then dG = -RTlnK

To calculate the equilibrium constant for the given reaction, we need to use the concept of Gibbs free energy (ΔG). The equilibrium constant (K) is related to ΔG through the equation:

ΔG = -RT ln(K)

Where ΔG is the Gibbs free energy change, R is the gas constant (8.314 J/(mol⋅K)), T is the temperature in Kelvin, and ln denotes the natural logarithm.

First, let's convert ΔGf° for BrCl(g) from kJ/mol to J/mol by multiplying it by 1000:

ΔGf° (BrCl(g)) = -1.0 kJ/mol * 1000 J/kJ = -1000 J/mol

At equilibrium, ΔG for the reaction is zero. Now we can rearrange the equation and solve for K:

ΔG = -RT ln(K)

Since ΔG = 0:

0 = -RT ln(K)

Divide both sides of the equation by -RT:

ln(K) = 0

Take the exponential function (e) of both sides to eliminate the natural logarithm:

e^(ln(K)) = e^0

K = 1

Hence, the equilibrium constant (K) for the given reaction is 1 at 25°C.