One of the best-selling light, or low-calorie, beers is 4.2% alcohol by volume and a 355-mL serving contains 110 Calories; remember: 1 Calorie = 1000 cal = 1 kcal. To estimate the percentage of Calories that comes from the alcohol, consider the following questions. (a) Write a balanced chemical equation for the reaction of ethanol, C2H5OH, with oxygen to make carbon dioxide and water. (b) Use enthalpies of formation in Appendix C to determine ΔH for this reaction. (c) If 4.2% of the total volume is ethanol and the density of ethanol is 0.789 g/mL, what mass of ethanol does a 355-mL serving of light beer contain? (d) How many Calories are released by the metabolism of ethanol, the reaction from part (a)? (e) What percentage of the 110 Calories comes from the ethanol?

Video transcript

Hi everyone for this problem. It reads wine on average has 11.6% alcohol by volume and a bottle contains 615 calories. On average, calculate the percentage of calories that come from alcohol and wine. Use the questions below to arrive at the answer. So we have a five part series here. So let's go ahead and get started with part one. Part one reads write a balanced chemical equation for the reaction of ethanol with oxygen to make carbon dioxide and water. Okay, so let's go ahead and get started with this part. So for part one we need to write a balanced chemical reaction and so we have ethanol reacts with water to give carbon dioxide and water. Okay, But the thing is we need to make sure this is balanced. Okay, so we're going to go ahead and write in these blanks here to make sure that we write the correct coefficients. Okay, so let's go ahead and start by looking at our number of carbons. Okay, so on the left side of our equation in our ethanol, we have two carbons. So let's go ahead and add a two to our carbon dioxide here by adding that to, We now have two carbons on the left and two carbons on the right by adding that to in front of our carbon dioxide, that now gives us three oxygen's on the right side. Okay, and so we need to put a three here in front of this oxygen gas. So now our number of oxygen atoms match on both left and right. Alright, so now we can look at our number of hydrogen. Okay, so on the left side we have six hydrogen by looking at our ethanol. So we need six on the right and in order for us to have six on the right, we need to add a three here. Okay. And so now We are balanced. This is a one. Okay. And you can confirm by counting up all of the elements, but this is the balanced equation. So let's go ahead and move on to the next part. Part two. Okay, part two asks us to use entropy of formation to determine the entropy of the reaction in part one. Okay, so in order for us to find the entropy of the reaction, we're going to need to know what the standard entropy of formations are for everything in our problem or in our equation. So these are values. We're going to have to look up. So let's go ahead and look up those values. So our standard heat of formation for ethanol Is equal to negative 2,777.7 killing girls. Our standard heat of formation of oxygen gas is zero because anything in its elemental state has a heat of formation of zero. Our standard heat of formation of carbon dioxide is equal to negative 393.5 kg jewels. And our standard heat of formation of water and we need to look at the state that it's in. It's a liquid state. So this is negative 285.83 Killah jewels. So now that we know what our standard heats of formation are, we can calculate the standard entropy change by taking the difference between our products and our reactant. Okay, so our standard entropy change for our reaction is going to equal the sum of our products minus the sum of our reactant. So we're going to take the number of moles for our products and react ints and multiply it by their standard heats of formation to get our standard entropy change for the reaction. Okay, so what that looks like Is so we'll start off with our products. So we have two moles of carbon dioxide. The standard heat of formation of carbon dioxide is negative 393.5 kill a jules Plus we have three moles of Water. And its standard heat of formation is negative. 285.83 Killah Jewels. So that's the sum of our products minus the sum of our reactant. So we have one mole of Of our ethanol. So we have one times its standard heat of formation is negative, 2777.7 Kill it jules plus we have three moles of oxygen. Gas but it's standard heat of formation is zero. So we just put a zero there. Okay, so this is our some of our products minus our some of our reactant. So we get a standard entropy change for our reaction. When we plug this into our calculator, it's going to equal negative 1366. killer jewels. So this is the answer to part two. So let's just highlight our final answers for each of the parts. So for part one, This was our answer for part two. This was our answer. So let's go ahead and move on to part three. Okay, so for part three, we're told to calculate the mass of ethanol and an average bottle of wine if 11.6% of the total volume is ethanol and the density of ethanol is 0.789 g per milliliter. Okay, so we want to calculate the mass of ethanol, which means we're going to need grams. Our final answer is going to be grams of ethanol. Let's go ahead and start off with what we know. Okay. And what we know is our our bottle of the volume Of our bottle is 25.4 oz. So let's go ahead and start there. So we have 25.4 oz. And we want to calculate the mass of ethanol. Okay, so we want to go from ounces, two mL. That way we can use the density that was given. Were told the density is 20.789 g per milliliters. So we need to go from 24.25 point four ounces to middle leaders in order to use that density? So let's do that now. So in one ounce there is 29. mL. Okay, so as you can see here are ounces cancel. And we're left with milliliters. So now we can use the density that was given. Okay. The density says although density given is one male leader per 7.789 g. Okay, so now our middle leaders canceled. Remember our goal here is we want the massive ethanol in grams. But we need to multiply this this by our Our percentage 11.6% of the total volume. Okay, so we're going to take whatever we get from that and multiply it by 0.116. Okay, So when we do that, we're going to get a mass of 68.75 g of ethanol. Okay, so this is going to be our answer for part three of this problem. Alright, so let's go ahead and move on to Part four. Part four asks us to calculate the calories released from the metabolism of ethanol. Okay, so calories released. So what are we going to start with here? We're going to start with our massive ethanol, which we just calculated is 68.75 g. Okay. And what we want to do is go from grams of ethanol to calories. Okay, so what we want to do first is since we're in grams, we want to go from grams to moles. Okay, how do we do that? We go from grams to moles by using molar mass. So in one mole In one mole of ethanol, we have Looking at the Molar Mass, it's 46.07 g of ethanol. So now we have our grams canceled and we're left with moles. And remember our final goal is to go to calories. So now we're in moles and we know what our standard entropy change for the reaction is. That's how we're going to go from moles to kill a jules. So what we calculated in Part two is the conversion factor we're going to use to go from moles to kill a jules. Okay, so in one mole, our standard entropy change is 1366. kila jules. Okay, so now our units of moles cancel and we're left with killer jules. Remember remember our final goal is to go from grams to calories. So now we can use our conversion of calories and kill a jules to cancel out our killer jewels. So in one calorie there is 4. killer jewels. Okay, so now you can see our killer jewels cancel and we're left with calorie. Okay, so this is going to give us our answer for part four. Once we do this calculation we get .49 calories, That's four. for Part four. Okay, and lastly, Part five, which is the main question we're trying to answer here, Part five asked us to calculate the percentage of calories that come from alcohol and wine. So now that we know what our calories from Part four is, we'll divide this by How many calories we started with. So we have four, calories. And in the problem we're told that Wine on average has 11.6% alcohol by volume and a bottle contains 615 calories on average. So we're going to divide this by that 615 calories on average. And because we want a percentage, we're going to go ahead and multiply this by 100%. Okay, so when we do this calculation, we get 79.3% which is going to be our final answer, four part five and the final answer for the main question of this problem. Okay, so that is it. And that is the end of this problem. I hope this was helpful