Question

You have an ideal gas in a container fitted with a frictionless, massless piston. What if you add weight to the top of the piston? We would expect the gas to be compressed at a constant temperature.

For these to be true, ∆S would be negative (since the gas is compressed), and ∆H would be zero (since the process is at constant temperature). This would make ∆G positive. Does this mean the isothermal compression of the gas is not spontaneous? Defend your answer.

Short answer

Yes, the isothermal compression of the gas is not spontaneous.

Step-by-step solution

what is a spontaneous process?

In thermodynamics, spontaneous processes are those which take place by themselves without any external force. For example, the flow of water from the hill, rusting of iron, rolling of balls from the hill, etc.

Just like the above examples most of the chemical reactions are spontaneous and some are non-spontaneous.

Step 2;To find the spontaneity in any chemical reaction, the three main factors are: change in entropy (∆S), change in enthalpy (∆H) and Gibbs free energy (∆G).

The relation between the above three factors is:

According to the second law of thermodynamics for the spontaneous process:

the entropy of the universe is always positive andGibbs free energy (∆G) is always negative

ΔG Negative → spontaneous

ΔG zero → equilibrium

ΔG Positive → non-spontaneous

therefore, if ∆S is negative (since the gas is compressed), and

∆H is zero (since the process is at a constant temperature).

This would make ∆G positive which means the isothermal compression of the gas is not spontaneous.