[jstorm064]

I am trying to tackle an entropy change problem involving temperature change and phase transition, but I am not getting the right answer.
I am asked to calculate the total ΔS for 2.0 moles of Pb, where the temperature is increased from 298 K to 923 K given that -
ΔH_fus = 4770 J mol^-1 at 600 K and S°_m = 64.8 J mol^- K^-.
I am also given the molar isobaric heat capacities for Pb for the liquid and solid phases -
C_p,m(s) = 22.1 J mol^- K^- and C_p,m(l) = 32.5 J mol^- K^-

To tackle this, I add the entropies of the temperature change with each heat capacity and the entropy at fusion -
[tex]\Delta S=\int_{T_{i}}^{T_{f}}\frac{C_{p}(s)}{T}dT + \frac{\Delta H_{fus}}{T_{fus}}+\int_{T_{i}}^{T_{f}}\frac{C_{p}(l)}{T}dT[/tex]

I plug 298 K for T_i and 923 K for T_f.

I keep getting 139 J mol^- K^-, which is not the right answer. Is there anything wrong with my expression for ΔS?

Thanks so much!

[cseil]

I am trying to tackle an entropy change problem involving temperature change and phase transition, but I am not getting the right answer.
I am asked to calculate the total ΔS for 2.0 moles of Pb, where the temperature is increased from 298 K to 923 K given that -
ΔH_fus = 4770 J mol^-1 at 600 K and S°_m = 64.8 J mol^- K^-.
I am also given the molar isobaric heat capacities for Pb for the liquid and solid phases -
C_p,m(s) = 22.1 J mol^- K^- and C_p,m(l) = 32.5 J mol^- K^-

To tackle this, I add the entropies of the temperature change with each heat capacity and the entropy at fusion -
[tex]\Delta S=\int_{T_{i}}^{T_{f}}\frac{C_{p}(s)}{T}dT + \frac{\Delta H_{fus}}{T_{fus}}+\int_{T_{i}}^{T_{f}}\frac{C_{p}(l)}{T}dT[/tex]

I plug 298 K for T_i and 923 K for T_f.

I keep getting 139 J mol^- K^-, which is not the right answer. Is there anything wrong with my expression for ΔS?

Thanks so much!

You shouldn't consider Ti and Tf as 298K and 923K.

You have to consider that entropy is a state function.
To calculate the entropy change you can imagine (in this case) three processes to arrive at the final state.

As I can see, you imagined these:

1) solid, 298 K -> solid, 600K
2) solid, 600K -> liquid, 600K
3) liquid, 600K -> liquid 923K

So, considering this. Are you sure that in the first integral Ti is 298K and Tf is 923?
Same question for the second integral.

Then: heat capacities and ΔH refers to 1 mol. Do you have just one mol in your problem?

[unsu]

What is the correct answer?
I got ΔS=37.42 J mol^-1 K^-1

For 2 mol Pb, ΔS=74.84 J mol^-1

[cseil]

What is the correct answer?
I got ΔS=37.42 J mol^-1 K^-1

For 2 mol Pb, ΔS=74.84 J mol^-1

I believe you forgot to add the S^o_m which is the entropy that a mole of Pb has at 298K.

[jstorm064]

You shouldn't consider Ti and Tf as 298K and 923K.

You have to consider that entropy is a state function.
To calculate the entropy change you can imagine (in this case) three processes to arrive at the final state.

As I can see, you imagined these:

1) solid, 298 K -> solid, 600K
2) solid, 600K -> liquid, 600K
3) liquid, 600K -> liquid 923K

So, considering this. Are you sure that in the first integral Ti is 298K and Tf is 923?
Same question for the second integral.

Then: heat capacities and ΔH refers to 1 mol. Do you have just one mol in your problem?

Gah! You're absolutely right. I didn't account for the fusion temperature and evaluated both integrals from 298K to 923K.

I got the solution from my prof - the correct answer is then 204.4 J K^-

Thanks for the assistance!