If ammonia is manufactured at 356 K, is the reaction spontaneous, given that the enthalpy and entropy change for the reaction are -93 kJ/mol and -198 J/mol K, respectively?

A. Yes, the ΔG is -92 kJ/mol.
B. No, the ΔG is 92 kJ/mol.
C. No, the ΔG is 22.5 kJ/mol.
D. Yes, the ΔG is -22.5 kJ/mol.

yes, it is spontaneous at -22.5 kJ/mol

dG = dH - TdS

dG = -93 - 356(-0.198) = ?
If - it's spontaneous?

Well, let me think about it... Ah, I've got it! Picture this: Ammonia is like a shy little molecule that pretends to be spontaneous at parties, but deep down it's actually quite calculated.

Now, the formula for Gibbs free energy (ΔG) is ΔG = ΔH - TΔS. So, to figure out if the reaction is spontaneous at 356 K, we need to plug in the numbers.

Given that ΔH = -93 kJ/mol and ΔS = -198 J/mol K, we can convert the latter to kJ/mol K by dividing by 1000. That gives us ΔS = -0.198 kJ/mol K.

Now, let's crunch the numbers. Subtracting TΔS, we get ΔG = -93 kJ/mol - (356 K * -0.198 kJ/mol K).

Calculating that gives us ΔG ≈ -93 kJ/mol + 70.488 kJ/mol. And after all that math, we find that ΔG is approximately -22.5 kJ/mol.

So, to answer your question, the correct answer is D. Yes, the ΔG is -22.5 kJ/mol. It seems like ammonia's spontaneous nature depends on the temperature. It's like a mood ring that changes with the environment!

To determine whether the reaction is spontaneous at 356 K, we need to calculate the Gibbs free energy change (ΔG) and compare it to zero. The equation for calculating ΔG is:

ΔG = ΔH - TΔS

Where:
ΔG is the Gibbs free energy change
ΔH is the enthalpy change
ΔS is the entropy change
T is the temperature in Kelvin

Given that:
ΔH = -93 kJ/mol
ΔS = -198 J/mol K
T = 356 K

First, convert the entropy change from J/mol K to kJ/mol K:
ΔS = -198 J/mol K = -0.198 kJ/mol K

Now, substitute the values into the equation for ΔG:

ΔG = -93 kJ/mol - (356 K * -0.198 kJ/mol K)
= -93 kJ/mol + (70.488 kJ/mol)
= -22.512 kJ/mol

Since the ΔG value is negative (-22.512 kJ/mol), this means the reaction is spontaneous.

Therefore, the correct answer is option D: Yes, the ΔG is -22.5 kJ/mol.

you have to work backwards

try all of the answers:
dG = -22.5 = -93 - (-198 x T)
= -22.5 + 93 = - (-198 x T)
= 70.5 = 198 x T
= 0.356 = T

we see that C is the only answer that works