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The reduction of iron (III) oxide with hydrogen produces iron metal and can be written as follows

Jules Bruno
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Hey, guys, In this new video, we're gonna take a look at the calculations behind Gibbs Free Energy. So if we take a look, at example, when it says the reduction of iron three oxide with hydrogen produces iron metal and keep the richness follows. So we have one mole of iron, three oxide, solid reacting with three moles of hydrogen gas to give us two moles of iron solid plus three moles of water vapor. I give you the Delta H or entropy value and the Delta s entropy value. The question says, Is this reaction spontaneous under standard state conditions at degrees Celsius? If not at what temperature will it become Spontaneous. So this is a two part question. So they're asking us if it's spontaneous or not. Remember, the best variable to calculate spontaneity is Delta G. So I gave you Delta H I gave you. Delta asked, and we have temperature so we can use Delta G zero equals Delta H zero minus t Delta s zero. And we know we should use this version because I'm saying standard state conditions. So we're supposed to use Delta G with a zero. So what we need to do next is we have to make sure that our Delta H and R Delta s values agreeing Units here, Delta H uses killer jewels, but Delta s uses jewels now. Killer jewels are the default type of units for these types of questions. So let's just convert the Delta s tequila jewels as well. So remember, we're gonna say, for every 1000 jewels there is one killer Joel. So this is equivalent to 0.141 five killer jewels over K. So we're gonna plug in the 98.8 killer. Gul's minus temperature has to be in Kelvin as well. So I had to 73.15 to 25. That gives us 2 98 15 kelvin times a Delta s value we just calculated. Okay, so the Kelvin's will cancel out. So to be killer jewels minus killer jewels. When we do that, we get a answer off 56.633 Killah jewels. Now, remember, if Delta G is negative, then it's going to be spontaneous. The fact that we got a positive answer means that this reaction is not spontaneous. So now it's up to us. to figure out what temperature will it become? Spontaneous. Now, anytime they ask you, at what temperature does it become Spontaneous. That means you assume that Delta G zero is equal to zero. Okay, so we're gonna use this this same exact equation here, except now, Delta G is zero, and that's still equals the same value for Delta H. The same value for Delta s here. We're not gonna know what temperature is. That's what we're trying to solve. So zero equals 98.8 killed. Jewels minus T times 0.1415 Killer jewels over K. What we're gonna do First, we're going to subtract out the 98.8 killer Joel's. And that equals negative tee times. Point won't 0.1415 killer jewels over K. We need to isolate temperature by itself. So we're gonna divide out negative 0.1415 killer jewels over K on both sides. So this cancels out with this, and the negative sign also cancels out. So we have a negative getting divided by another negative. Kelly jewels. Cancel out. Our answer will be in Kelvin. So the temperature here equals 6. 98.233 temperature. Now, technically, if we take that number and plug it back in, then Delta G will equal zero. Remember, when Delta G equals zero were at equilibrium or technically, still not spontaneous. So what you would say is temperatures above this answer would give you a spontaneous reaction. Okay, so we're gonna say temperatures above this answer would be spontaneous temperatures below it would be non spontaneous. So make make careful. Sure. Like when you're looking at your exam, what exactly are they're asking you in terms of temperature? Are they looking for an exact answer or they asking, um, at what temperature will it be? Spontaneous. Just remember, when you work it out, the temperature you get, that's technically the temperature at equilibrium. So all you have to say is any temperature above that, whether it be like 0.1 uh, degrees higher, it's still gonna be spontaneous. It'll just be a little bit spontaneous. Okay, so remember the answer. You get temperatures above that answer will make your reaction spontaneous. Now that we've done example one together, I want you guys to attempt to do practice one here were saying, If Delta G is small and positive, which of the following statements is true? And I'll give you guys a huge hint. Remember, we have to think of Delta G in three situations when it's less than zero equal to zero or greater than zero. What do each of those mean? What do I mean by the word small? Also, remember, if you're spontaneous one way, then you'll be non spontaneous the other way. Just because Delta G is positive doesn't mean it can't be spontaneous, period. It would be non spontaneous in the Ford. What about the reverse? Ask yourself these questions and you'll be able to answer this question really quickly. Good luck, guys.