Using information in Appendices B and C, calculate the minimum grams of propane, C3H8(g), that must be combusted to provide the energy necessary to convert 5.50 kg of ice at -20 °C to liquid water at 75 °C

Video transcript

Hello everyone today. We are being given the following problem and asked to solve for it, It says a 4.52 kg of ice at negative 10°C must be converted to liquid water at 80°C. What mask of plantain must be combusted to provide the energy required for this process. So this is a multi step problem. And the first step that we need to solve for this question is we need to find the heat which is denoted by that equation of ice, Which is going to go from negative 10°C to ice at 0°C. And why is that? Well? 0°C is the freezing point for water. And so to do that, that's what we must convert it to. And so we have our Q equals M C delta T. And so essentially we can rewrite this equation to look like this. We can say that the heat is equal to the mass times our specific heat capacity or c times our change in our temperature. So that's going to be our final temperature minus our initial temperature. We have our mass when presented to us 5.44 point 52 kg. Which we need to convert this into regular grams. So if we take 4.52 kg and we use the conversion factor that 10 to the negative third kilogram. Or if we use the conversion factor that for one kg we have 10 to the third grams. We have 404, g. And so we're gonna go ahead and plug that into our equation here. 4520g. The specific heat capacity for water of course is going to be two 108 and it's going to be units of jewels per grams times Celsius. And then lastly we have a change of temperature. Our final temperature is going to be 0°C and our initial temperature is going to be negative 10°C. Plugging this into our calculator, we will get a total value of 95, and 81.6 jewels. When we convert this into killer jewels by using the conversion factor that 10 to the third jewels equals one kg jule. We get a final answer of 95.28 kg joules. But we're not done yet. Our second step is going to be to find the in therapy Of our fusion reaction infusion is going from our ice at 0°C to liquid water At 0°C. So we're going from solid to liquid. That's fusion. And so we have this delta H. Fusion abbreviated as fus. We're in we take our mass our g and we multiply that by our 3 34 jewels program when our units cancel out, this is going to give us an answer of 1,509, jewels. But of course our units must be in kill jules. So we're going to use the conversion factor that one kill a jewel is equal to 10 to the third jewels. In which we get an answer of 1509.68 kg joules. Our 3rd step is going to be to solve for our heat from when we go from a liquid At 0°C, so liquid at 0°C to a liquid at 80°C from the question step. And so we're gonna use our heat is equal to our mass once again which is 4520 g. Where they're gonna multiply by our specific heat of liquid water which is 4.184. And of course this is in units of joules per grams times cm. And they're gonna multiply this by our change in temperature which are final temperature is 80°C And our initial temperature is 0°C. So when we saw for Q we're going to get that Q. Is equal to one million 512, 5020.4 jewels. And once again are units are in kilo joules. So we can use the conversion factor that want to kill the jewel is equal to 10 to the third jewels. And when we do this we end up with an answer of 1512 or 1512. kg jewels. We then must calculate Q total. So we say that Q total or our total heat. We take what we sold from in step one which was our 0.28 kg joules. And we added to what we solved in step three hour Step two, which would be our 1509. So 1509.68 kg joules. And that gives us a total of 3,117.9 kg jewels. Our last and final step Step four is going to be to calculate our delta H combustion or the combustion of the heat of the reaction for painting. And so if you're right at the top right here, we have that our plantain C five H 12 and gas form is going to react with our eight moles of oxygen in the gas form as well To provide us five moles of CO2 in the gas form and six moles in water, which is also in the gas form. And so doing this, we know that this is equivalent to products minus reactant. And so what does that mean? We're going to solve this, we're going to solve for our combustion for our products and we're going to subtract that from the combustion of our reactant. So, for products, what we do is we are going to take the delta H for our first product C 02, which is going to be negative 3 93. kg per mole. And we're going to multiply that by how many moles of that we have, which is five moles of that CO2. And we take we use that using the coefficient that is present in front of that CO2. And they were going to go ahead and add that to our other Product that we have, which is water, and that's going to be negative 241. Kg per mole by that. By how many moles of that we have, which is six moles. And we're going to subtract that by our heat of combustion for our reactant, which for our painting is going to be negative 146. kg joules per mole and we only have one. So we can just say multiplied by one mole. And then lastly, we're going to add that to our zero kg per mole that we have for our oxygen gas. Oxygen gas always has a zero kg per mole. And so our final answer is going to be negative 300 or 3,271.4 kg per mole. But we're not quite done yet for our last and final step to find the mass needed of plantain. We're gonna go over here, we're gonna say step five. What we want to do is we want to take our molar mass of painting C five H 12, which of course is going to equal 72.146 g per mole. And then we want to take to find the total mass of our plantain C H12. We're going to take the mass that we calculated in the previous portion of our question. Which was that in question in step three, Which is was that 3117.9 kg joules. We're then gonna multiply by what we just sold for. We're gonna use a multi ratio and say that one mole of plantain is going to equal our 3271.4 kg joules that we just saw it for in step four. And then lastly, we're going to multiply by the molar mass. And we're gonna say that one mole of plantain on the denominator so that our units can cancel Is equal to 72.146 g to yield us a final mass of 68.8 g. I hope this helped. And until next time