An exothermic reaction is spontaneous above 400K but non spontaneous below it. Of the deltaH for the reaction is -40.0 kcal, what are the values of deltaS and deltaG at 400K?

dG = dH - TdS

dG = 0 at 400; i.e., the dividing line between spontaneity and non-spontaneity.
dH = 40,000, T = 400 K, solve for dS.

If G=0 and I solve the equation for dS it would be

S= 0/(400 x 40,000).
Anything divided by 0 is zero. How can I get a value for dS?

Your algebra needs improving.

dG = 0
dG = dH-TdS
0 = dH - TdS
TdS = dH - 0
TdS = dH
dS = dH/T = ?

To find the values of deltaS and deltaG at 400K, we can use the relationship between deltaG, deltaH, and deltaS given by the equation:

deltaG = deltaH - T * deltaS

where deltaG is the change in Gibbs free energy, deltaH is the change in enthalpy, deltaS is the change in entropy, and T is the temperature in Kelvin.

We are given that the deltaH for the reaction is -40.0 kcal, and we know that deltaG is related to deltaH and deltaS at a given temperature. Now, since the reaction is exothermic and spontaneous above 400K but non-spontaneous below it, we can infer that deltaG must be negative (spontaneous) above 400K and positive (non-spontaneous) below it.

At 400K, we substitute the values into the equation:

deltaG = -40.0 kcal - (400K * deltaS)

Now, rearrange the equation to solve for deltaS:

deltaS = (-deltaG + 40.0 kcal) / 400K

Since we know that deltaG is negative at 400K, the equation simplifies to:

deltaS = (40.0 kcal + abs(deltaG)) / 400K,

where abs(deltaG) represents the magnitude of deltaG.

So, to find the value of deltaS at 400K, plug in the value of deltaG into the equation. However, without additional information specifying the exact value of deltaG, we cannot determine the precise value of deltaS at 400K.