It is quite common for a solid to change from one solid state structure to another at a temperature below its melting point.
For example, sulfur undergoes a phase change from the α-orthorhombic form (S8; density≅2.07 g/cm3) to the β-monoclinic form (S8; density≅2.00 g/cm3) as it is warmed above 95.3 °C.
Assuming that ΔH for this phase change is 0.442 kJ/mol, calculate ΔS for this phase change.
For a reaction, dG = dH - TdS
Assuming the phase change is at 95.3, then dG @ equilibrium = 0. Plug in dH and T and solve for dS.
Well, well, well, looks like sulfur is quite the shape-shifter! Let's calculate the entropy change, shall we?
First, we need to convert ΔH from kJ/mol to J/mol, because entropy likes to play in the SI unit sandbox. So, ΔH would be 0.442 kJ/mol * 1000 J/kJ = 442 J/mol.
Now, we can use the equation ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, T is the temperature in Kelvin, and ΔS is the entropy change.
Since the phase transition occurs below the melting point, we can assume that ΔG = 0.
0 = 442 J/mol - (95.3 + 273.15)K * ΔS
Now let's solve for ΔS:
ΔS = 442 J/mol / (95.3 + 273.15)K
Calculating that out gives us approximately ΔS = 1.01 J/(mol*K).
So, the entropy change for sulfur's little transformation dance is about 1.01 J/(mol*K).
Now that's some serious solid-state shape-shifting action!
To calculate ΔS (change in entropy) for a phase change, we can use the equation:
ΔG = ΔH - TΔS
where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
Given that ΔH = 0.442 kJ/mol and the phase change occurs at 95.3 °C, we need to convert the temperature to Kelvin:
T = 95.3 + 273.15 = 368.45 K
Now we can rearrange the equation to solve for ΔS:
ΔS = (ΔH - ΔG) / T
Since the phase change occurs at a constant temperature, ΔG = 0 (since ΔG = ΔH - TΔS, and at equilibrium, ΔG = 0). Thus:
ΔS = ΔH / T
Plugging in the values:
ΔS = 0.442 kJ/mol / 368.45 K
Calculating this value, we get:
ΔS = 0.001200 kJ/(mol·K)
Therefore, the ΔS for this phase change is approximately 0.001200 kJ/(mol·K).
To calculate the entropy change (ΔS) for a phase change, you can use the equation:
ΔS = ΔH / T
Where:
ΔS is the entropy change
ΔH is the enthalpy change
T is the temperature in Kelvin
In this case, we know the ΔH is 0.442 kJ/mol. However, the equation requires temperature in Kelvin, so we need to convert 95.3 °C to Kelvin.
To convert Celsius to Kelvin, you can use the formula:
T(K) = T(°C) + 273.15
So, converting 95.3 °C to Kelvin:
T(K) = 95.3 + 273.15 = 368.45 K
Now, we have all the values we need to calculate ΔS:
ΔS = ΔH / T = 0.442 kJ/mol / 368.45 K = 0.00120 kJ/(mol·K)
Therefore, the ΔS for this phase change is approximately 0.00120 kJ/(mol·K).