How do you calculate ΔSfus and ΔSvap for HCl given melting point,ΔHfus, boiling point, and ΔHvap

also how do you determine the entropy change when 5.20 mol of HCl(l) freezes at atmospheric pressure.

dG = dH-TdS. At the melting point, dG = 0 (dG always 0 at equilibrium conditions)

rearrange to dS = dH/T..
Boiling point don the same way but substitute dHvap for dHfus and different T.

To calculate ΔSfus (change in entropy of fusion) and ΔSvap (change in entropy of vaporization) for HCl, you need the melting point (Tfus), the enthalpy of fusion (ΔHfus), the boiling point (Tvap), and the enthalpy of vaporization (ΔHvap).

Step 1: Calculate ΔSfus:

ΔSfus = ΔHfus / Tfus

Step 2: Calculate ΔSvap:

ΔSvap = ΔHvap / Tvap

To determine the entropy change when 5.20 mol of HCl(l) freezes at atmospheric pressure:

Step 1: Calculate the amount of heat released during freezing using the enthalpy of fusion:

Heat released during freezing = ΔHfus * moles of HCl

Step 2: Use the formula:

ΔS = Heat released during freezing / T

Where T is the temperature at which the freezing occurs. In this case, it is the melting point of HCl.

So, ΔS = (Heat released during freezing) / Tfus

Plug in the values and calculate to find the entropy change.

To calculate the entropy changes ΔSfus (the entropy of fusion) and ΔSvap (the entropy of vaporization) for HCl, you need to use the equations:

ΔSfus = ΔHfus / Tfus
ΔSvap = ΔHvap / Tvap

Where:
ΔHfus is the heat of fusion (in J/mol)
Tfus is the melting point temperature (in K)
ΔHvap is the heat of vaporization (in J/mol)
Tvap is the boiling point temperature (in K)

To determine the entropy change when 5.20 mol of HCl(l) freezes at atmospheric pressure, you need to use the equation:

ΔS = ΔSfus * n

Where:
ΔS is the entropy change (in J/K)
ΔSfus is the entropy of fusion (in J/K·mol)
n is the number of moles of the substance

Here's how you can calculate the entropy changes and the entropy change during freezing:

Step 1: Convert the given melting and boiling point temperatures to Kelvin (K).

Step 2: Calculate ΔSfus using the equation ΔSfus = ΔHfus / Tfus, where ΔHfus is given and Tfus is the melting point temperature you converted to Kelvin.

Step 3: Calculate ΔSvap using the equation ΔSvap = ΔHvap / Tvap, where ΔHvap is given and Tvap is the boiling point temperature you converted to Kelvin.

Step 4: Calculate the entropy change during freezing using the equation ΔS = ΔSfus * n, where ΔSfus is from Step 2 and n is the number of moles of HCl(l), which is 5.20 mol.

Note: Make sure to use the correct units when plugging in the values into the equations, and pay attention to whether the enthalpy values are given per mole or per mole of substance being transformed.

For #2, I assume you have tables.

HCl(l) ==> HCl(s)
dSrxn = dSproduct - dSreactant
That will give you dS/mol, then multiply by 5.20 mols.