[orgo814]

"Glucose and fructose are simple sugars with the molecular formula C6H12O6. Sucrose, or table sugar, is a complex sugar with molecular formula C12H12O11 that consists of a glucose unit covalently bound to a fructose unit (a water molecule is given off as a result of the reaction between glucose and fructose to form sucrose). a) Calculate the energy released as heat when a typical table sugar cube of mass 1.5 g is burned in air. b) To what height could you climb on the energy a table sugar cube provides assuming 25 percent of the energy is available for work? c) The mass of a typical glucose tablet is 2.5 g. Calculate the energy released as heat when a glucose tablet is burned in air d) To what height could you climb on the energy a cube provides assuming 25 percent of the energy is available for work?

I figured out how to solve for the energy (q). My plan was to look up the enthalpy of combustion for each quantity. So for the first part, find the delta H combustion for sucrose and use H = U + PV (deltaNg RT) to solve for the delta Uc (which should be equal to delta Hc since there is no change in moles and I'm assuming T is constant at 298 K). After that I can find q by q=(n)(deltaU combustion). However, I do not understand how to find the height. It almost sounds like a physics problem which I would use kinematics for. Since work was mentioned I'm assuming their is some relation there however I cannot figure it out. Any insight would be greatly appreciated.

[Yggdrasil]

For a chemical reaction performed at constant pressure, the amount of heat released (q) is equal to the change in enthalpy of the reaction (ΔH).  ΔU would have additional contributions from the work performed by the system, so you want to calculate ΔH in order to find the heat released.

For the height question, you are converting heat energy into potential energy (gravitational potential energy) by lifting an object.  Do you remember an equation that relates the gravitational potential energy of an object to its height?

[orgo814]

Do I need to convert to potential energy first? I think the equation is PE= Mass x gravity x height? Is my method for the first part right.. Since I was solving for q which is equal to delta H... My plan being to look up the enthalpy of combustions given in my text, then use that to find delta U by delta H= delta U + deltaN(gas)RT (again I'm assuming there's no change in gaseous molecules so it is is equal to delta H combustion). Since the balanced equation is c6h12o6 + 6o2 yields 6CO2 + 6H2O and only gaseous molecules are O2 and CO2. Then using that delta U to find q by multiplying its absolute value by the number of moles.

[orgo814]

And I'm assuming I'd need to multiply my q by .25 before using that energy height equation

[Yggdrasil]

Do I need to convert to potential energy first? I think the equation is PE= Mass x gravity x height? Is my method for the first part right.. Since I was solving for q which is equal to delta H... My plan being to look up the enthalpy of combustions given in my text, then use that to find delta U by delta H= delta U + deltaN(gas)RT (again I'm assuming there's no change in gaseous molecules so it is is equal to delta H combustion). Since the balanced equation is c6h12o6 + 6o2 yields 6CO2 + 6H2O and only gaseous molecules are O2 and CO2. Then using that delta U to find q by multiplying its absolute value by the number of moles.

ΔU = q + w, so in general, you should not use ΔU to find q.  Instead, you should use enthalpy because for reactions performed at constant pressure ΔH = q.

And I'm assuming I'd need to multiply my q by .25 before using that energy height equation

Yes.

[orgo814]

Ok. How do I know we're at constant pressure though since they never said that in the problem? And should I just find the standard reaction enthalpy (enthalpy products - enthalpy reactants).. Which is the enthalpy of combustion. Sorry for all the questions. If I do that I'm assuming delta U isn't helpful for this problem

[Yggdrasil]

Most reactions in the lab are performed in containers open to the atmosphere (e.g. burning sugar in air), which will keep the reaction at constant pressure (atmospheric pressure).  On the other hand, if you were to perform the reaction at constant volume (e.g. in a sealed container), ΔU = q.

Yes, you just need to look up the enthalpies of combustion of sucrose and glucose then use those to calculate q.

[orgo814]

And those enthalpies of combustion would be equal to Q at cP. thanks for the help

[orgo814]

Sorry to be a pain- but once I have my Q calculated from my delta H (delta H= Q) do I need to convert Q to W before using the equation PE= mgh?

[Yggdrasil]

assuming 25 percent of the energy is available for work

That's all that's needed for conversion.

[orgo814]

So I can just multiply my heat energy by .25? Never knew that

[Yggdrasil]

No, it depends on the details of how exactly your heat engine is converting heat into work, but since the problem states the efficiency of the heat engine, you can just use that value.