For potassium metal, the heat of fusion is 2.33KJ/mol, and the entropy of fusion is 6.93 J/mol-K. At what temperature does potassium melt?

http://en.wikipedia.org/wiki/Entropy_of_fusion

To determine the temperature at which potassium melts, we need to use the equation:

ΔG = ΔH - TΔS

Where:
ΔG is the change in Gibbs free energy
ΔH is the enthalpy change (heat of fusion)
T is the temperature
ΔS is the change in entropy

We know the heat of fusion (ΔH) is 2.33 kJ/mol, which can be converted to J/mol by multiplying it by 1000:
ΔH = 2.33 kJ/mol = 2330 J/mol

The entropy of fusion (ΔS) is given as 6.93 J/mol-K.

Now let's substitute these values into the equation:

ΔG = 0 at the melting point, so we can set it as zero:
0 = ΔH - TΔS

Next, rearrange the equation to solve for the temperature (T):

TΔS = ΔH

T = ΔH / ΔS

Substitute the values:
T = 2330 J/mol / 6.93 J/mol-K

Perform the calculation:
T ≈ 336.44 K

Therefore, potassium melts at approximately 336.44 Kelvin (K).