How much ice (in grams) would have to melt to lower the temperature of 352 mL of water from 25 °C to 5 °C? (Assume the density of water is 1.0 g/mL.)

Video transcript

Hello everyone in this video, we're going to deal with the Q E M C delta T. Formula. So the question is asking us to determine the mass of ice that must melt. To cool a certain amount of water From 30°C to 3°C. So let's first recognize our cute equals M. C delta T. Equation. So our Q. Here that stands for heat energy and this whole formula is what we call a specific heat formula. So first in this problem we're gonna go ahead and solve for the heat energy of water. So I just put QH 20. And that equals of course the M. C delta T. Delta T. Is just going to be, let's put this off to his side. Delta T stands for the change in temperature. That's just T final. So the final temperature minus T. I. So initial temperature. Alright, so moving on so we have the mass who's going to be 500 grams C. Stands for the specific key capacity And of water that's going to be four .18 jewels programs times Celsius. And then our delta T. Like I said over here in this asterix here, The T final is going to be three and R. T final R. T initial is going to be 30. All right now, of course our units the graham's going to cancel the grams This right here is that we can say is just one unit of degree Celsius. So that cancels as well and we're just left with jules. So putting all these numbers into my calculator I'll get a total of negative 5600 or sorry, 56,430 jules. Now for the second part, I'm going to go ahead and calculate for the hit energy of our ice. So I just put cute ice and that's actually going to equal to negative Q. Of Our Water H. 20. And also but is going to be equal to of course our M. Cat equation regarding our ice plus the mass of our ice times the delta H. Of fusion social F. U. S. Alright, so continue with this formula then will have this negative and our negative Q. H. 20. We saw for over here. So let's go ahead and rewrite that. All right, so that's going to go ahead and equal to the m times the specific heat of Ice, which is the same thing as the water. So it's going to be 4.18 jules and eat her grams times degree Celsius. And the delta T. It's going to be the T. Final. So that's three degrees Celsius. Now, because we're talking about the ice And of course the initial temperature of our ice is going to be 0°C. Then of course we're adding this mess and then the smaller mass of our water is oh two g. Let me just go ahead and actually write this sloping lower because we need our one more on top Divide by the 18th. So two grubs. Alright And then we're going to not apply that by six point two killer jewels over one more and I'll just go ahead and continue this on the bottom. And what we're just going to do here next is going to convert that killer jewels right here and two jewels. So we're going to multiply everything By 10 to the 3rd tools. Mhm One killed again. That's just to cancel our units and converts the killer jewels and the jewels. Right? So once I put everything here into my calculator and I just go ahead and also scroll down. All right, Then I'll get a positive five or 56, 430 jewels and that will equal to 12.54 jules program times are um plus 334.073 jules program and again, times. So now we're just gonna go ahead and solve for R. M. S. And once I go ahead and do that, I will actually find out that m He goes to 162.80 gramps and that is going to be my final answer for this problem. Thank you all so much for watching