For the reaction described by the chemical equation:

3C2H2(g) -> C6H6(l) .. Delta H rxn = -633.1 kJ/mol
a) Calculate the value of Delta S rxn at 25.0 C...
b) Calculate Delta G rxn...
c) In which direction is the reaction, as written, spontaneous at 25 C and 1 bar pressure?
- forward, reverse, neither, or both?

here's what i did:
Delta S = [1(173.4 J/mol-k)] - [3(200.9)]
Delta S = -429.3 J/mol-k

Delta G = Delta H - T(Delta S)
Delta G = (-633.1 kJ/mol) - (298 K)(-0.4293 kJ/mol-k) = -505.168 kJ/mol

if that's right so far.. yay! but can someone explain how a reaction can be spontaneous forwardly or reversely? right now i only know that a reaction is spontaneous if delta G is a negative number.. please help!

Actually it is forward, not neither, since it is less than 0. I just answered this question on a quiz and it showed me the correct answer.

Oh I understand. If dG = 0 .. would that make the reaction direction neither? When would it ever be both?

I didn't confirm the numbers you quote by looking in a table but other than that the process looks ok. The question may be worded a weird way but it makes sense if you know what it's asking. You know, as you pointed out, that the reaction is spontaneous if dG is <0. What if dG>0? That simply means the reaction is not spontaneous in the direction written BUT it is spontaneous in the REVERSE direction. That's what the problem means by forward or reverse. Any reaction that is spontaneous in one direction you can categorically say is not spontaneous in the reverse direction.

Oh okay trick question then thanks again dr bob!

Well, congratulations on your calculations so far! You're on the right track.

Now, let's talk about spontaneity. A reaction can be spontaneous in either the forward or reverse direction, depending on the values of enthalpy (ΔH) and entropy (ΔS).

If ΔG is negative, it means the reaction is spontaneous in the direction as written. In this case, the reaction is more likely to proceed from left to right (forward direction), resulting in the formation of benzene (C6H6). So, the forward reaction is spontaneous.

However, if ΔG is positive, it means the reaction is not spontaneous in the direction as written. It indicates that the reverse reaction (from right to left) is more favorable. But in this case, since ΔG is negative, we know that the forward reaction is spontaneous.

So, in conclusion, a reaction can be spontaneous both forwardly and reversely, depending on the values of ΔG. It's all about which direction is favored energetically.

Hope this clarifies things for you!

Great job on calculating the values of ΔS rxn and ΔG rxn! Your calculations are correct.

Now, to answer your question on the direction of spontaneity of a reaction, it is important to understand the concept of Gibbs free energy (ΔG).

Gibbs free energy is a thermodynamic parameter that combines the effects of enthalpy (ΔH) and entropy (ΔS) to determine the overall spontaneity of a chemical reaction. It quantifies the maximum amount of work that can be obtained from a system at constant temperature and pressure.

When ΔG is negative, it indicates that the reaction is spontaneous in the forward direction. This means that the reactants will tend to combine and form products. In your case, a negative ΔG value for the reaction 3C2H2(g) -> C6H6(l) suggests that the formation of benzene (C6H6) is favored when starting with acetylene (C2H2).

Conversely, when ΔG is positive, it means that the reaction is non-spontaneous in the forward direction. This indicates that the products will tend to decompose into reactants.

Additionally, when ΔG is equal to zero, the reaction is at equilibrium, with no net change in the concentrations of reactants and products.

It's important to note that the direction of spontaneity of a reaction can also depend on temperature and pressure. In your case, since the temperature is given as 25°C (or 298 K) and the pressure is not mentioned, we assume it to be at 1 bar pressure.

So, in summary, when ΔG is negative, the reaction is spontaneous in the forward direction, and when ΔG is positive, the reaction is spontaneous in the reverse direction. If ΔG is zero, the reaction is at equilibrium.

I hope this helps clarify the concept of reaction spontaneity! Let me know if you have any further questions.

Yes, dG = 0 is neither. When dG = 0 the system is at equilibrium and there is no net reaction in either direction.

If a reaction is spontaneous in one direction it is automatically non-spontaneous in the reverse direction. There never will be a situation in which it is spontaneous in both directions unless you want to argue the fine point that when dG = 0 it is proceeding both forward and reverse (however, there is no net reaction and I hardly call that spontaneous but I guess in the strict sense, and taken literally, you could argue that it is).