An 8.5-g ice cube is placed into 255 g of water. Calculate...

Name: Problem 69, Chapter 11: Chemistry A Molecular Approach
Uploaded: 2019-06-16T21:41:04-08:00
Duration: 7 min 30 s
Channel: Lucas Pressley
Description: An 8.5-g ice cube is placed into 255 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.

An 8.5-g ice cube is placed into 255 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.

Key Concepts

Latent Heat of Fusion

This is the energy required to change a substance from its solid phase to its liquid phase at constant temperature. In the context of this problem, it describes the amount of energy needed to melt the ice, which must be supplied by the water, resulting in a decrease in the water's temperature.

Specific Heat Capacity

This is a property of a material that defines the amount of energy required to raise the temperature of a unit mass of the substance by one degree. It is used here to determine how much the temperature of the water decreases when it loses a given amount of energy to melt the ice.

Conservation of Energy

This principle states that energy cannot be created or destroyed but only transferred. In this scenario, the energy lost by the warmer water is exactly equal to the energy gained by the ice to change its phase, ensuring the overall energy remains constant.

Heat Transfer

This concept involves the transfer of thermal energy from one object or medium to another. In this case, heat is transferred from the warmer water to the colder ice until the ice completely melts, which results in a reduction in the water's temperature.

Transcript

00:01 So i've written down a couple of variables that we should know.

00:05 So we're given the mass of the ice, which is 8 .5 grams, and the mass of the water, which is 255 grams.

00:11 And we're trying to find the change in temperature, which i've listed here is kind of the unknown right now.

00:18 So when you think about just logically what's happening, you're taking a chunk of ice and putting it in water, and so what's going to happen? the ice is going to melt, and it'll take some heat.

00:28 We'll call that q1, which is the amount of heat needed to melt the ice.

00:31 Ice and make it water and then that corresponding water is going to heat up and match the temperature of the water that was in the cup so we'll call that q2 and q3 and that will equal zero due to conservation of energy so now we just need to figure out what these three are so q1 is the melting of the ice and that's just equal to the moles of water times delta h of fusion or the moles of ice and delta h fusion is a constant given in your textbook as 6 .02 kilojoules per mole.

01:25 Now note we were given ice and grams, so i have to convert that to moles.

01:30 So you just do 8 .5 grams, about a molar mass of water, which is 18 .01 grams per.

01:47 And now give us 0 .47 moles of water.

01:57 So q1 is equal to 0 .472 times 6 .02 kilo2 kilojoules per mole.

02:15 And this is moles right here.

02:18 So the moles will cancel out and we'll be given a number of 2 .84 kilojoules.

02:30 So we got our q1.

02:32 Now we need to get our q2 and our q3.

02:36 So q2 is equal to m, c, delta, t.

02:46 And so this is the mass of water times the heat capacity of water times the change in temperature...