Consider a substance X with a ΔHvap =20.3 kJ / mol and ΔHf u s=9.0 kJ / mol. The melting point

step 1 Okay, so this question is about the behavior of the liquid. Let's first read the question. Consi

Consider a substance X with a ΔHvap =20.3 kJ / mol and ΔHf...

Consider a substance $\mathrm{X}$ with a $\Delta H_{\text {vap }}=20.3 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta H_{f u s}=9.0 \mathrm{~kJ} / \mathrm{mol}$. The melting point, freezing point, and heat capacities of both the solid and liquid $\mathrm{X}$ are identical to those of water. If you place one beaker containing $50 \mathrm{~g}$ of $\mathrm{X}$ at $-10^{\circ} \mathrm{C}$ and another beaker with $50 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$ at $-10^{\circ} \mathrm{C}$ on a hot plate and start heating them, which material will reach the boiling point first? Which of the materials from part a, $\mathrm{X}$ or $\mathrm{H}_{2} \mathrm{O},$ would completely boil away first? On a piece of graph paper, draw the heating curve for $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{X}$. How do the heating curves refleet your answers from parts a and $\mathrm{b}$ ?

Consider a substance $\mathrm{X}$ with a $\Delta H_{\text {vap }}=20.3 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta H_{f u s}=9.0 \mathrm{~kJ} / \mathrm{mol}$. The melting point, freezing point, and heat capacities of both the solid and liquid $\mathrm{X}$ are identical to those of water.

If you place one beaker containing $50 \mathrm{~g}$ of $\mathrm{X}$ at $-10^{\circ} \mathrm{C}$ and another beaker with $50 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$ at $-10^{\circ} \mathrm{C}$ on a hot plate and start heating them, which material will reach the boiling point first? Which of the materials from part a, $\mathrm{X}$ or $\mathrm{H}_{2} \mathrm{O},$ would completely boil away first? On a piece of graph paper, draw the heating curve for $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{X}$. How do the heating curves refleet your answers from parts a and $\mathrm{b}$ ?

Key Concepts

Specific Heat Capacity

This concept refers to the amount of energy required to raise the temperature of a given mass of a substance by one degree Celsius. In the context of heating curves and phase changes, the specific heat capacity determines the slope of the temperature rise in each phase (solid, liquid, or gas) before a phase transition occurs. In this problem, both substances have the same specific heat capacity as water, which means that the energy required to raise their temperatures from -10°C to 0°C, or from 100°C upward, is identical.

Latent Heat of Phase Transitions

Latent heat is the amount of energy absorbed or released by a substance during a phase change at a constant temperature. There are two kinds: latent heat of fusion for solid–liquid transitions and latent heat of vaporization for liquid–gas transitions. The problem highlights that substance X has different ?Hfus and ?Hvap compared to water, even though their temperature milestones (melting and boiling points) are the same. This difference in latent heat influences the amount of energy needed for each phase change, altering the overall heating curve and determining which substance reaches boiling sooner or evaporates completely first.

Heating Curve

A heating curve is a graphical representation that shows how a substance’s temperature changes as heat is added, including plateaus that represent phase transitions. The segments where the temperature remains constant correspond to the energy being used for phase changes (e.g., melting or boiling) rather than increasing temperature. In the problem, both water and substance X exhibit similar temperature increases due to identical specific heats and phase transition temperatures, but differences in the latent heat values result in differing lengths of the plateau regions on the heating curve, thereby influencing how quickly each substance reaches the boiling point and is completely vaporized.

Transcript

00:01 Okay, so this question is about the behavior of the liquid.

00:08 Let's first read the question.

00:10 Consider a substance x with the entropy of the vaporization is 20 .3 kilojou per more.

00:26 And the entropy of the fureen is nine kilojou per more.

00:39 The melting point, freezing point, and heat capacity of both solids and liquid acts are identical to those of water.

00:53 Melting point, boiling point, and heat capacity, same as water.

01:11 And then the first question is, if you place one beaker containing 50 grams of the axe and 50 grams of water, both at minus 10 degree c on a hot plate and start heating them, which material will reach the bottom point first.

01:39 So before we answer this question, it's a comparison between the x and water.

01:47 So then we need to know the value of the water for both the entropy of the furean and the entropy of the vaporization.

01:55 So you can check the book.

01:57 You will find for water, the entropy of the vaporization is actually around 17 .4 kilojou per more, which is smaller than the liquid x.

02:19 And it's heat of fiorin for water.

02:24 It's actually 6 .01 kilojou per more, which is also smaller than the, i would say, smaller than the liquid x.

02:45 So, okay, so you ask us if we start heating them, which material will reach the boiling point first.

02:54 So at minus 10 degrees c, we will know that both cases, since they have the same melting point and boiling point, at minus 10 degree c, both x and water are in the liquid phase.

03:19 And if you want to reach the boiling point, sorry, it's not in the liquid phase.

03:25 It's actually in the solid phase at the beginning and minus 10.

03:33 So if you want to reach the boiling point, the solid will first melt into the liquid and then continue to increase the temperature until reach the boiling point.

03:49 So let's write down the process.

03:52 So first it needs to go from minus 10 to 0 degree c.

03:57 At this point, it melts.

04:00 And then the boiling point is 100 degrees c.

04:04 And this situation, it's the boiling point.

04:10 They ask which one actually will reach the boiling point first.

04:16 So basically ask which one actually consume less heat because it requires less heat, you probably can heat it to the boiling point first.

04:30 So it mentions actually for heat capacity.

04:34 When for heat capacity, they are the same.

04:39 So before the melting, the energy that are consumed from 10 degree to 0 degree actually is the same for both.

04:48 And also from 0 to 100 before reaching the boiling point is also the same, the energy they consumed because they have the same heat capacity.

04:59 Why the difference actually comes from this process.

05:04 The melting because the melting does not change the temperature but it continuously actually consume the heat so if during the melting which no matter which one actually consume less energy actually will actually go to the boiling point faster so you actually need to find the one who actually consume less energy for the heating, for the melting.

05:49 So basically you want to compare the d .hf, the heat of the urine, which one has the lowest heat of the fuel.

06:02 And if you do a comparison, you'll find actually the water has the lowest, lower value of the heat of the fueling...

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