An ice cube tray contains enough water at 22.0^∘ C to make 18 ice cubes that each has a mass of

step 1 So here we have 18 ice cubes and there are 30 grams each. So we can just times these together to

An ice cube tray contains enough water at 22.0^∘ C to make...

An ice cube tray contains enough water at $22.0^{\circ} \mathrm{C}$ to make 18 ice cubes that each has a mass of 30.0 $\mathrm{g} .$ The tray is placed in a freezer that uses $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ as a refrigerant. The heat of vaporization of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ is 158 $\mathrm{J} / \mathrm{g}$ . What mass of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ must be vaporized in the refrigeration cycle to convert all the water at $22.0^{\circ} \mathrm{C}$ to ice at $-5.0^{\circ} \mathrm{C} ?$ The heat capacities for $\mathrm{H}_{2} \mathrm{O}(s)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ are 2.03 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and 4.18 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ , respectively, and the enthalpy of fusion for ice is 6.02 $\mathrm{kJ} / \mathrm{mol} .$

Key Concepts

Calorimetry and Energy Balance

Calorimetry involves measuring the amount of heat exchanged in physical and chemical processes. In problems involving multiple temperature changes and phase transitions, an energy balance is set up to account for all the heat absorbed or released. This balance ensures that the energy removed from one system is equal to the energy absorbed by the other, following the principle of conservation of energy.

Refrigeration Cycle and Refrigerant Vaporization

The refrigeration cycle is a process used to remove heat from a system, often by employing a refrigerant. The cycle takes advantage of the refrigerant's heat of vaporization, meaning that as the refrigerant vaporizes, it absorbs a significant amount of heat from the surroundings. This principle is exploited in cooling systems to lower the temperature of a target substance.

Specific Heat Capacity

This concept refers to the amount of energy required to raise or lower the temperature of a unit mass of a substance by one degree Celsius. In thermodynamic calculations, it is used to determine the heat absorbed or released during the temperature change of materials, both when heating/cooling liquids and solids.

Latent Heat (including Enthalpy of Fusion and Vaporization)

Latent heat is the energy absorbed or released during a phase change without a change in temperature. This concept encompasses the heat of fusion, which is the energy required to change a substance from solid to liquid (or vice versa), and the heat of vaporization, which is the energy needed for the substance to change from liquid to gas (or vice versa). Understanding these values is crucial for calculating energy exchanges in phase transitions.

Transcript

00:01 So here we have 18 ice cubes and there are 30 grams each.

00:06 So we can just times these together to get the amount, the total amount of water that we have in the tray, which is 540 grams of h2o.

00:21 And so first we need to figure out how much heat is required to, or how much energy is required to freeze this water.

00:33 And then we can use that energy and use the heat of vaporization for the cf to cl2 to then find how many grams we need of that to vaporize to do this process.

00:55 So first we have water.

00:58 We have liquid water.

00:59 So let's put water.

01:01 And we need to get that to zero degrees celsius first.

01:05 So first, it's at 22 degrees celsius to start.

01:12 So we need to get that, so we need to reduce that to zero degrees now.

01:18 So we can use q equals mc delta t.

01:24 Let me make that a little bit neater.

01:27 M .c.

01:27 Delta t.

01:29 And so we know mass, the mass, we already found that out, 540 grams.

01:36 And we know the specific heat of water.

01:39 Which is given in the problem, liquid water, and then conveniently you'll see that the grams cancel out and the temperature cancels out and it's 22 degrees because 22 minus 0 is 22.

01:56 And that gives us after rounding for sig -figs 49 ,700 joules.

02:06 So now since we have all of our water, liquid water at zero degrees, now we need to have the phase change.

02:14 So we need to go to from water...

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