[DexterQ]

I have this particular set of questions in my chemistry textbook problem:

A Large portion of metabolic energy arises from the biological combustion of glucose:
   
C₆H₁₂O₆(s) + 6O₂(g)  ->  6CO₂(g) + 6H₂O(g)

(a) If this reaction is carried out in an expandable container at 37 degrees Celsius and 780 torr, what volume of CO₂ is produced from 20.0 g of glucose and excess oxygen?

(b) If the reaction is carried out at the same conditions with the stoichiometric amount of oxygen, what is the partial pressure of each gas when the reaction is 50% complete (10 g of glucose remains)

For part (a):
I assumed that there should be a remaining amount of the excess oxygen after the reaction, but then there is no given information about the oxygen amount to calculate the partial pressure of the leftover oxygen, so I cannot solve for it to find the partial pressure of carbon dioxide. However, if I used the given pressure, I would get 16.5 Liters, which is also the answer from the textbook. Why is that? Does the expandable container has anything to do with the partial pressure of the two gases?

For part (b):
The stoichiometric amount of oxygen is 2/3 (mol), and the amount of Oxygen reacted is 1/3 (mol). I arrived with 1/3 (mol) for the vapor water and carbon dioxide as well. Then I calculated the molar fraction for the carbon dioxide, vapor water and the remaining oxygen amount that hasn't reacted, which results in a fraction of 1/3 for each gas. This would give the partial pressure of each gas to be (780 torr/3) = 260 torr. The answer from the textbook, however, is 48.8 torr for the vapor water, and 3.7x10² torr for the oxygen and carbon dioxide. Was there a flaw in my calculation or in my assumptions?

Thanks in advance for the help.

[mjc123]

a) You are right to use the given pressure. The question is equivalent to asking: by how much does the volume of the expandable container increase at constant pressure due to the production of CO₂? That is equal to the volume that amount of gas would occupy at that pressure. Of course, within the container the gases are mixed, and the partial pressure of CO₂ is 780*16.5/V torr, where V is the total volume. V litres at this pressure is equivalent to 16.5 L at 780 torr.

b) 48.8 torr is the saturation vapour pressure of water at 37°C. If you have a higher pressure of water vapour than this, it will condense to liquid, so the amount of water vapour is limited.

[Big-Daddy]

b) 48.8 torr is the saturation vapour pressure of water at 37°C. If you have a higher pressure of water vapour than this, it will condense to liquid, so the amount of water vapour is limited.

How did you work this out? (Or rather how did the book expect students to work this out!)

Or did you just "know" that at 37°C, saturation vapour pressure of water is 48.8 torr? 

[DexterQ]

Could you please clarify a bit more? I don't think I have quite understood it. By the end of the reaction, there would be the leftover oxygen and the carbon dioxide product in the tank. Wouldn't the 780 torr of pressure be composed of the two partial pressures of the gases? And wouldn't the total volume be the total of the original volume plus the increase volume by carbon dioxide? Thanks and I'm sorry for being a bit slow on this because partial pressure is confusing for me.

a) You are right to use the given pressure. The question is equivalent to asking: by how much does the volume of the expandable container increase at constant pressure due to the production of CO₂? That is equal to the volume that amount of gas would occupy at that pressure. Of course, within the container the gases are mixed, and the partial pressure of CO₂ is 780*16.5/V torr, where V is the total volume. V litres at this pressure is equivalent to 16.5 L at 780 torr.

[mjc123]

How did you work this out? (Or rather how did the book expect students to work this out!)

Or did you just "know" that at 37°C, saturation vapour pressure of water is 48.8 torr? 

I looked it up on wikipedia, fount of all knowledge . didn't  find exact value at 37 °C, about 42 at 35°C, but close enough. I think they expect you to have the physical nous to realise what's going on, even if you don't have the vp-T curve of water memorised! And to be able to look these things up.

Could you please clarify a bit more? I don't think I have quite understood it. By the end of the reaction, there would be the leftover oxygen and the carbon dioxide product in the tank. Wouldn't the 780 torr of pressure be composed of the two partial pressures of the gases? And wouldn't the total volume be the total of the original volume plus the increase volume by carbon dioxide? Thanks and I'm sorry for being a bit slow on this because partial pressure is confusing for me.

Physically, yes, the pressure in the container comprises the sum of the partial pressures of the gases, which each occupy the whole volume, because they are completely miscible. It is rather artificial to express the amount of gas as a volume at the total pressure (as if this amount of gas were generated instantly, before mixing with the other gases), but it is often done, especially when the conditions are constant pressure and expandable volume.

[Big-Daddy]

I looked it up on wikipedia, fount of all knowledge . didn't  find exact value at 37 °C, about 42 at 35°C, but close enough. I think they expect you to have the physical nous to realise what's going on, even if you don't have the vp-T curve of water memorised! And to be able to look these things up.

Ah, so essentially the value had to be looked up. Thank God. I was wondering if I had completely misunderstood what is and is not possible to calculate from the data in the OP in the context of this problem.