∆S phase change from liquid to solid

Question

Determine ∆S for the phase change of 2.52 moles of water from liquid to solid at 0.0 °C. (∆H = -6.01 kJ/mol)

Answer 1

Given:

ΔH_solid(H₂0)= -6.01 kJ/mol(H₂0)

n H₂0 = 2.52 mols H₂0

T = 0.0^o C = 273 K

2.52 mols H₂0 * -6.01 kJ/mol(H₂0)

2.52 mols H₂0 * -6.01 kJ/mol(H₂0)

2.52 * -6.01 kJ = -15.1452 kJ

ΔH_solid(H₂0)= -15.1 kJ (mols was given with 3 significant figures)

ΔS = ΔQ/T

ΔS = -15.1 kJ/273 K = -0.0553 kJ/K

-0.0553 kJ/K * 10³ K/kJ = -55.3 J/k (units of ΔS are J/K)

Since temp was given to 2 significant figures:

Answer:

ΔS =-5.5 x 10¹ J/K

Answer 2

To solve this question, you will want to review the 2nd law of thermodynamics which states that "the entropy of an isolated system increases for a spontaneous process". It can also be described mathematically. In its simplest form this equation is ∆S≥q/T.

In your question, you are given both the enthalpy (∆H) and the amount of water. Enthalpy is the heat (q) per mole, so you can find the heat, by multiplying the moles you were given by the enthalpy. Like this:

-6.01 kJ/mol * 2.52 mol = -15.15kJ.

-15.15kJ is the heat released when that specific amount of water freezes. (q)

Assuming that the water is frozen reversibly, the change in entropy will be ∆S=q/T (it its not reversible ∆S>q/T). So, we can plug in the q we calculated above and divide it by the temperature that water freezes at. It's important to note that the units of entropy are J/K, so the temperature needs to be in kelvin.

Water freezes at 0.0°C. To convert this to kelvin, we add 273.15. This makes the temperature needed 273.15K.

∆S=q/T

= -15.15kJ / 273.15K

= -0.0554 kJ

Entropy usually is measured in J/K, so we can convert the kJ to J. 1000 joules equals 1 kJ, so we can convert our answer to J by multiplying by 1000 J/ 1 kJ.

∆S= -0.0554 kJ/K (1000J/1kJ)

= -55.4 J/K

At this point, it is always helpful to take a minute to ask yourself if your answer makes sense. Remember that entropy is a measure of molecular randomness. So, as a substance transitions from a liquid phase to a solid phase, the amount of disorder in the system decreases. This is because solids are more ordered than liquids on the molecular level. Because in this question the water is freezing, we would expect the entropy to decrease, so the change in entropy can be expected to be negative, which is what we calculated!