A 10.5-g ice cube at 0°C is placed into 245-g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

Video transcript

Hello. Everyone in this video, we're gonna deal a lot with our Q. Equals M. C. Delta T. Equation is also known as the equation or the specific heat formula. The Q. Right over here. That stands for heat energy. Alright, so let's go ahead and get started then. So first here we have to recognize some things. These things I have gone from either textbook or maybe your professor has given this values to you as well. Well let's just put kind of like a key here. See All right, so Mikey. So Delta H. Of fusion just as F. U. S. Of water. So h. That's going to equal to 6.01 killer jewels per mole. And then the specific heat capacity of water. So H. 20. That's going to equal to 4. jewels per grams times Celsius. And lastly the molar mass Of H. 20. Is going to equal to 18.02 g per mole. Alright, so now we can officially start now that we have this key set up for us. So again, we're doing our Q. Equals M. C. Delta T. Equation. This time we're talking about ice. So my cute ice is going to equal to well first we have that five g because M. is equal to mass. So we have this five g. I'm gonna go ahead and cancel our gram to get moles. How we can do this is by using the molar mass the molar mass of ice which is just water is going to be 18.02 g on top or on the bottom on top is going to be one more. Then I'm gonna go and multiplied by the specific heat capacity of water Or the Delta Age fusion of water in our case, that's going to be 6.01 kill jules her. Then I'm gonna go ahead and convert this killer jewels here to Jules. So I'm going to continue it kind of like a dimensional analysis problem. So we'll have 10 to the third jewels per one killer jewel. Alright, I'm putting everything into my calculator. My queue of ice is going to be 1,667. jules. Alright now second part now is to recognize that we need to find our queue of HDL. So Q. of H. 20. Is actually equal to the negative Q. Of ice which we just offered. So but just plug it in and then our queue of H 20 is just negative 1667. jules. Alright, now that we have the Q H20. We can actually put this back here in the equation and just solve for our kind of our delta T here but a little broken apart because you know that delta T. Is T final minus T. Initial. Alright, so let's just go ahead and actually scroll down a little bit here. Alright, so like I said we're utilizing our cue echoes M C. Delta T equation again. This time we actually have that Q value. So plugging it in. We have one negative 1,667. jewels. And we have our mass of 1 g. The specific heat capacity of water is 4.18 joules per grams times degree Celsius. And of course has multiplied by our delta T. Value. So putting everything into my calculator. I'm solving for delta T. I get that delta T. Is equal to negative 2.6596 degrees Celsius. And are they said before this delta T. Value is going to equal to my T. Final. So the final temperature minus our initial temperature. So T. I. Or T. Initial. Alright, so now following this here then we have that are negative 2. degrees Celsius is equal to. Again, we're solving for T. F. T. Final so T F minus R. Eight degrees Celsius. That is solving for R. T. F. We will get that the final temperature is going to be equal to 5.3404. All right. And the last part here, just bringing in that my cube of ice is equal to negative Q. Of H. 20. So water basically like this which is switched backwards. So breaking this down to know that what the Q even represents. We have our M. C. Times T. F. F minus T. Initial T. Of ice equals to negative M. C. Again T. F. F. And then minus T. Of H. 20. All right now plugging numerical values again I'm just gonna scroll down a little bit. Alright let's put in numerical values. So our mass. We have five g specific heat capacity is 4.18 jewels programs, times degree Celsius. Then we have our unknown T. F. F -0°C. And that's going to equal to the negative parentheses 150 g which is the mass. There's a specific key capacity. Same thing for for 18 jewels per grams times degree Celsius. And of course melting pie ng all of this by just simply write delta T. And kind of simplifying this. Then we'll get 20.9 times t. f. f equals turn negative 627. You know expanding this here, We'll Get T. F. F -5.3404. Now just solving for R. T. F. F. Here I will find that my T. F. F. Is equal to 5.17 degrees Celsius. And that is going to be my final temperature. Alright hopefully this helped you. All. Good luck