How much heat (in kJ ) is needed to convert 866 g of ice at -10^∘ C to steam at 126^∘ C ? (The s

How much heat (in kJ ) is needed to convert 866 g of ice at...

How much heat (in $\mathrm{kJ}$ ) is needed to convert $866 \mathrm{g}$ of ice at $-10^{\circ} \mathrm{C}$ to steam at $126^{\circ} \mathrm{C} ?$ (The specific heats of ice and steam are $2.03 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and $1.99 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ respectively.)

Key Concepts

Specific Heat Capacity

This is a material property that indicates the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius without a phase change. It is crucial for calculating the heat needed to raise or lower the temperature of a substance in a given process.

Latent Heat

Latent heat refers to the amount of heat absorbed or released by a substance during a phase change at constant temperature. It includes the latent heat of fusion, which is needed to change a substance from solid to liquid, and the latent heat of vaporization, required for changing from liquid to gas.

Phase Transitions

Phase transitions are processes where a substance changes from one state of matter to another, such as from solid to liquid (melting) or from liquid to gas (vaporization). These transitions require energy input or output, which is calculated separately from specific heat calculations since the temperature remains constant during the change.

Sequential Energy Calculations

This concept involves breaking down a complex thermal process into several steps (such as heating, phase change, and further heating) and calculating the heat required for each step individually. The total energy change is then obtained by summing the heat values for all stages.

Transcript

00:01 To approach this question, we're going to consider each of the different cues that we're going to have taking place as this transition occurs.

00:09 So starting off, we have solid water, which then we heat up from starting at negative 10 degrees celsius, which is going to go all the way until we hit the transition point, which is solid water at zero degrees celsius.

00:36 Which is then going to turn to liquid water, which is also at 0 degrees celsius.

00:46 And then that is going to heat all the way up until we have liquid water at 100 degrees celsius, which is then going to turn into steam or gaseous water, which is also at 100 degrees celsius.

01:07 And lastly, that is going to go to gaseous water.

01:14 Sorry, this should be gaseous, not liquid, which is going to be at 126 degrees celsius.

01:24 So we're going to denote this qs for solid.

01:31 This is going to be qf for fusion.

01:35 This is going to be ql for liquid.

01:39 This is going to be qv for vaporization.

01:45 And lastly, we have qg.

01:46 For gaseous.

01:49 And what we need to find is q total, which is simply the sum of all of these things.

02:02 So let's go ahead and figure out what each of these are going to be.

02:14 Okay, starting with q solid, we're going to have 866 grams times 2 .03.

02:35 Jules per gram degree celsius times the temperature change, which we know for this is going to be 0 minus 10 degrees celsius.

02:58 And if we calculate that out, we're going to find that that equals 17 ,579 .8 joules.

03:11 Okay.

03:12 Next up qf for fusion we're given a molar value so we're going to need to convert this 866 grams into moles so we're going to multiply that by one mole per 18 .02 grams you can get this for water just right off your periodic table and then we're going to multiply this by by 6 ,010 joules per mole.

03:53 This is also 6 .01 kilojoules per mole, as you will find in your data table.

03:59 And that comes out to be 1 ,960 ,274.

04:14 274 joules.

04:17 And then we can move.

04:18 Move on now to the queue of our liquid...

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