Question

V. The element gallium freezes at 29.8 °C, and its molar enthalpy of fusion, DHfus = 5.59 kJ/mol. (a) When molten gallium solidifies at its normal melting point, is DS positive or negative. Briefly explain. (b) Calculate DS when 60.0 g of liquid gallium solidifies at 29.8 °C.

Answer 1

(a)

We know that the entropy dS = dQ /T

And the reaction is as follows:

Ga (l ) < == > Ga (s)

Given that dH   or DHfus = 5.59 kJ/mol

Thus for solidification dH = - 5.59 KJ/ mole or - 5590 J/mole

And temperature = 29.8 C or

29.8 +273 = 302.8K

Therefore,

dS = dQ /T

= - 5590 J/mole / 302.8K

= - 18.46 J / mole-K

Thus when molten gallium solidifies at its normal melting point, is DS negative.

(b)

Given that mass of Ga = 60.0 g

Now calculate the number of moles of Ga as follows:

Number of moles = amount in g / molar mass

= 60.0 g / 69.723 g / mole

= 0.861 moles

Then calculate the change in entropy as follows:

- 18.46J / mole-K * 0.861 mole

= - 15.89 J/ K