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Problem 60

In photosynthesis, plants form glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ and oxygen from carbon dioxide and water. Write a balanced equation for photosynthesis and calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ},$ and $\Delta G_{\mathrm{ren}}^{\circ}$ at $25^{\circ} \mathrm{C}$ . Is photosynthesis spontaneous?

Answer

$\Delta H^{\circ}=2802.5 \mathrm{kJ}$

$\Delta G^{\circ}=2878.6 \mathrm{kJ}$

$\Delta S^{\circ}=-259.5 \mathrm{J} / \mathrm{K}$

nonspontaneous

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## Discussion

## Video Transcript

So we're trying to calculate the gives free energy of photosynthesis and see this reaction spontaneous or non spontaneous. And so first thing you need to do is write out the equation of photosynthesis. So they tell you, Seo, too, plus water gets converted to Glucose, which is C six h, 12 06 purse. 602 And so I'll write this out again in the bottom. Thio include balancing this documentary, so we need to do some bouncing. And so it was just a refresher from previous chapters. So they're six carbons on the right. So let's put a six in front of CIA to to balance two carbons, and there's 12 carbons and the right and is like two currently. So I need to add a six in front of age to, uh, and so that that part's balanced. The next thing we need to count for us to oxygen. And so currently there's 18 oxygen on the left and only six oxygen from glucose, sending another 12 so you can get that from oh, too. So put a six in front of 02 There's no now that our reaction is balanced, we can start calculating the Ethiopian and entropy. So you do this by looking these values up in your textbook and then you for each of these molecules and then you do products minus reactant, accounting for Knowles. So, for example, for adult age, not glucose, it's minus one too. 773.3 plus six terms. Zero because oxygen is in its primary state. So that's your products. And you gotta subtract your your reactivates. So you subtract six comes 3 93 point of close six terms negative to 85.8. And so once you add all that up, you're left with 28 2.1 killer Jules, because I was important. Keep tracking units. So next we'll calculate entropy. Same way you can find these values in the same appendix in your textbook. Said this would do to 12 point one. So this is your products. Urine cipri values free products from six times to, uh, 0.2 minus six times to 13.8 plus six times 70. And so when you carry that through, you're left with a negative to 59. 25 Jules Per Calvin. And so now that we have that, we can calculate gives for energy. And we're told this reaction occurs at 25 degrees Celsius. Dr. G goes that the H dynasty of s so he cools to 802.1. And so this isn't killed. Jules and Entries and Joel. So after Kember for that minus 2 98 Kelvin times negative to 59. 25 over 1000. Put that in Killer Jules. And so while that gets us is 2807 9 killed Jules. And so then you can ask, Is this reaction spontaneous or non spontaneous? And because the is positive, this reaction is non spontaneous. And so this makes sense because for photosynthesis to occur, you need some light, which is your source of energy to allow this reaction to occur.

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