[CHM 330] CHM 311 HW #3 Questions

[Andrew J. Pounds]

I rarely do this for homework problems, but since you seem to really be 
struggling with this, here is how I worked it...

ΔrS∘(T2)=ΔrS∘(T1)+∫T1T2ΔrCpdTT\Delta_rS^{\circ}\left(T_2\right) = 
\Delta_rS^{\circ}\left(T_1\right) + \int_{T_1}^{T_2} \Delta_rC_p\frac{dT}{T}
remembering that

ΔrCp=∑PRODnCp−∑REACTnCp

\Delta_rC_p = \sum^{PROD}n Cp - \sum^{REACT}n Now, rearranging...

ΔrS∘(T2)=ΔrS∘(T1)+[Cp(H2O)−Cp(H2)−12Cp(O2)]∫T1T2dTT\Delta_rS^{\circ}\left(T_2\right) 
= \Delta_rS^{\circ}\left(T_1\right) + \left[C_p(H_2O) - C_p(H_2) - 
\frac{1}{2} C_p(O_2)\right] \int_{T_1}^{T_2} \frac{dT}{T}

and integrating...

ΔrS∘(T2)=ΔrS∘(T1)+[Cp(H2O)−Cp(H2)−12Cp(O2)]lnT2T1\Delta_rS^{\circ}\left(T_2\right) 
= \Delta_rS^{\circ}\left(T_1\right) + \left[C_p(H_2O) - C_p(H_2) - 
\frac{1}{2} C_p(O_2)\right] \ln\frac{T_2}{T_1}
Now substituting terms...


ΔrS∘(323)=−44.49+[36.5−28.8−29.4/2]ln323298\Delta_rS^{\circ}(323) = 
-44.49 + \left[ 36.5 - 28.8 - 29.4/2\right] \ln\frac{323}{298}Answer: -45.05



On 1/26/22 14:05, wrote:
> Dr. Pounds,
>
> I worked the problem again using two calculators making sure that the 
> results of the intermediate steps are visible. Despite this, I'm still 
> ending up with -43.9 J/(mol*K) - (please see attached picture).
>
> Since the Mastering HW 3 is due Feb. 1^st  at midnight, when might be 
> a good time to stop by your office later this week or Monday/Tuesday 
> next week to review where I went wrong with this problem?
>
> Thank you,
>
> ------------------------------------------------------------------------
> *From:* Andrew J. Pounds <pounds_aj at mercer.edu>
> *Sent:* Tuesday, January 25, 2022 5:27 PM
>
> *Subject:* Re: CHM 311 HW #3 Questions
> I just did the problem myself and got the answer found in Mastering.  
> Can you show me your intermediate results?
>
> It looks like you are setting up the problem correctly, but either 
> through rounding or calculation error you final results are off.
>
>
>
>> Dr. Pounds,
>>
>> I double-checked my work in the previous image that I sent you (CHM 
>> 330 HW 3 Rev 3 - JM.JPG) and I used the following constant pressure 
>> specific heat capacities:
>>
>> 29.39 J/(mol*K) for O_2 (per your instructions)
>> 36.5 J/(mol*K) for H_2 O (given)
>> 28.85 J/(mol*K) for H_2  (based on book values)
>>
>> Using these constants results in a final answer for part 6b of -43.9 
>> J/(mol*K).
>>
>> The mistake I made on part 7b was forgetting to convert a number to 
>> kJ, but that conversion is not needed for part 6b. If the constant 
>> pressure specific heat capacities are correct, what else could be 
>> wrong? (I am reattaching revision 3 of my work for this problem for 
>> your convenience).
>>
>> Thanks,
>> Jonathan
>>
>> ------------------------------------------------------------------------
>> *From:* Andrew J. Pounds <pounds_aj at mercer.edu> 
>> <mailto:pounds_aj at mercer.edu>
>> *Sent:* Tuesday, January 25, 2022 2:57 PM
>>
>> *Subject:* Re: CHM 311 HW #3 Questions
>> To get the correct values in Mastering you must use the constants 
>> supplied by the text.  What happens if you use the value that I 
>> provided in my last e-mail for oxygen. The values that you showed me 
>> for the other compounds looked good.
>>
>>
>>
>> Dr. Pounds,
>>>
>>> I went ahead and verified that all three constant pressure specific 
>>> heat capacities match those listed on NIST and with the new value 
>>> you gave me. Substituting these values into the equation for 6b, I 
>>> get -43.9 J/(mol*K).
>>>
>>> I think I'm close, but Mastering still rejects that answer. What 
>>> should I do?
>>>
>>> Thanks,
>>>
>>>
>>>
>>>
>>>
>>> ------------------------------------------------------------------------
>>> *From:* Andrew J. Pounds <pounds_aj at mercer.edu> 
>>> <mailto:pounds_aj at mercer.edu>
>>> *Sent:* Tuesday, January 25, 2022 11:29 AM
>>>
>>> *Subject:* Re: CHM 311 HW #3 Questions
>>> The work looks reasonable, but you may want to check out the value 
>>> of the constant pressure specific heat capacity for oxygen.  I have 
>>> that as 29.39 J/mol.K
>>>
>>> See if that fixes things...
>>>
>>>
>>>> Dr. Pounds,
>>>>
>>>> Thank you for pointing those things out. I took another look at the 
>>>> homework and was able to understand / answer part 7b correctly.
>>>>
>>>> In addition, I realized (per your suggestion) that the temperature 
>>>> units should be Kelvin (absolute) and that my integrations were 
>>>> originally incorrect. However, despite having made these 
>>>> corrections, Mastering still marks part 6b incorrect. I believe 
>>>> there is a minor issue that I'm not catching, but I'm not sure what 
>>>> it is.
>>>>
>>>> Could you take another look at my revised work for part 6b and let 
>>>> me know what my error(s) is?
>>>>
>>>> Thank you,
>>>> Jonathan
>>>>
>>>> ------------------------------------------------------------------------
>>>> *From:* Andrew J. Pounds <pounds_aj at mercer.edu> 
>>>> <mailto:pounds_aj at mercer.edu>
>>>> *Sent:* Monday, January 24, 2022 3:19 PM
>>>>
>>>> *Subject:* Re: CHM 311 HW #3 Questions
>>>>
>>>>> Dr. Pounds,
>>>>>
>>>>> I have finished working all of the problems on HW 3 except for 6b 
>>>>> and 7b. Before sending you an email, I tried searching for similar 
>>>>> problems in the textbook but was unable to find any.
>>>>>
>>>>> For 6b, I used the formula we discussed in class today (please see 
>>>>> the attached document), but I might have interpreted 
>>>>> it incorrectly. Could you take a look at my work and let me know 
>>>>> where I made my mistake(s)?
>>>>>
>>>> What temperature units should you be using?
>>>>
>>>>
>>>>> For 7b, I attempted to use the equation we used in class today 
>>>>> (equation 3.30) for finding ΔG at non-standard conditions; 
>>>>> however, it appears to only be valid when there is a change in 
>>>>> temperature. Since the reaction in exercise 7b takes place at the 
>>>>> same standard temperature but at a different pressure, how does 
>>>>> this change Equation 3.30 - or is there another equation that 
>>>>> should be used?
>>>>>
>>>> To calculate the change on the Gibbs free energy as a function of 
>>>> pressure you will need to use equations from page 78 of the text.  
>>>> Since the acetaldehyde and carbon dioxide are both products in the 
>>>> reaction, they will appear in the numerator of the law of mass 
>>>> action (which we will start covering later this week).
>>>>
>>>>
>>>>> Thank you,
>>>>>
>>>>
>>>> -- 
>>>> *Andrew J. Pounds, Ph.D.*
>>>> /Professor of Chemistry and Computer Science/
>>>> /Director of the Computational Science Program/
>>>> /Mercer University, Macon, GA, 31207 (478) 301-5627 /
>>>
>>>
>>> -- 
>>> */Andrew J. Pounds, Ph.D./*
>>> /Professor of Chemistry and Computer Science/
>>> /Director of the Computational Science Program/
>>> /Mercer University, Macon, GA 31207 (478) 301-5627/
>>
>>
>> -- 
>> */Andrew J. Pounds, Ph.D./*
>> /Professor of Chemistry and Computer Science/
>> /Director of the Computational Science Program/
>> /Mercer University, Macon, GA 31207 (478) 301-5627/
>
>
> -- 
> */Andrew J. Pounds, Ph.D./*
> /Professor of Chemistry and Computer Science/
> /Director of the Computational Science Program/
> /Mercer University, Macon, GA 31207 (478) 301-5627/


-- 
*/Andrew J. Pounds, Ph.D./*
/Professor of Chemistry and Computer Science/
/Director of the Computational Science Program/
/Mercer University, Macon, GA 31207 (478) 301-5627/
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