# 5.3 Phase transitions in heating curves  (Page 7/21)

 Page 7 / 21

## Total heat needed to change temperature and phase for a substance

How much heat is required to convert 135 g of ice at −15 °C into water vapor at 120 °C?

## Solution

The transition described involves the following steps:

1. Heat ice from −15 °C to 0 °C
2. Melt ice
3. Heat water from 0 °C to 100 °C
4. Boil water
5. Heat steam from 100 °C to 120 °C

The heat needed to change the temperature of a given substance (with no change in phase) is: q = m $×$ c $×$ Δ T (see previous chapter on thermochemistry). The heat needed to induce a given change in phase is given by q = n $×$ Δ H .

Using these equations with the appropriate values for specific heat of ice, water, and steam, and enthalpies of fusion and vaporization, we have:

${q}_{\text{total}}={\left(m\text{⋅}c\text{⋅}\text{Δ}T\right)}_{\text{ice}}+n\text{⋅}\text{Δ}{H}_{\text{fus}}+{\left(m\text{⋅}c\text{⋅}\text{Δ}T\right)}_{\text{water}}+n\text{⋅}\text{Δ}{H}_{\text{vap}}+{\left(m\text{⋅}c\text{⋅}\text{Δ}T\right)}_{\text{steam}}$
$\begin{array}{}\\ \\ =\left(\text{135 g}\text{⋅}\text{2.09 J/g}\text{⋅}\text{°}\text{C}\text{⋅}15\text{°}\text{C}\right)+\left(135\text{⋅}\frac{\text{1 mol}}{18.02\phantom{\rule{0.2em}{0ex}}\text{g}}\text{⋅}\text{6.01 kJ/mol}\right)\phantom{\rule{0.2em}{0ex}}\\ +\left(\text{135 g}\text{⋅}\text{4.18 J/g}\text{⋅}\text{°}\text{C}\text{⋅}100\text{°}\text{C}\right)+\left(\text{135 g}\text{⋅}\frac{\text{1 mol}}{18.02\phantom{\rule{0.2em}{0ex}}\text{g}}\text{⋅}\text{40.67 kJ/mol}\right)\\ +\left(\text{135 g}\text{⋅}\text{1.84 J/g}\text{⋅}\text{°}\text{C}\text{⋅}20\text{°}\text{C}\right)\\ =\text{4230 J}+\text{45.0 kJ}+\text{56,500 J}+\text{305 kJ}+\text{4970 J}\end{array}$

Converting the quantities in J to kJ permits them to be summed, yielding the total heat required:

$=4.23\phantom{\rule{0.2em}{0ex}}\text{kJ}+\text{45.0 kJ}+\text{56.5 kJ}+\text{305 kJ}+\text{4.97 kJ}=\text{416 kJ}$

What is the total amount of heat released when 94.0 g water at 80.0 °C cools to form ice at −30.0 °C?

40.5 kJ

## Key concepts and summary

Phase transitions are processes that convert matter from one physical state into another. There are six phase transitions between the three phases of matter. Melting, vaporization, and sublimation are all endothermic processes, requiring an input of heat to overcome intermolecular attractions. The reciprocal transitions of freezing, condensation, and deposition are all exothermic processes, involving heat as intermolecular attractive forces are established or strengthened. The temperatures at which phase transitions occur are determined by the relative strengths of intermolecular attractions and are, therefore, dependent on the chemical identity of the substance.

## Key equations

• $P=A{e}^{-\text{Δ}{H}_{\text{vap}}\text{/}RT}$
• $\text{ln}\phantom{\rule{0.2em}{0ex}}P=-\frac{\text{Δ}{H}_{\text{vap}}}{RT}\phantom{\rule{0.2em}{0ex}}+\text{ln}\phantom{\rule{0.2em}{0ex}}A$
• $\text{ln}\phantom{\rule{0.2em}{0ex}}\left(\frac{{P}_{2}}{{P}_{1}}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{Δ}{H}_{\text{vap}}}{R}\phantom{\rule{0.2em}{0ex}}\left(\frac{1}{{T}_{1}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{T}_{2}}\right)$

## Chemistry end of chapter exercises

Heat is added to boiling water. Explain why the temperature of the boiling water does not change. What does change?

Heat is added to ice at 0 °C. Explain why the temperature of the ice does not change. What does change?

The heat is absorbed by the ice, providing the energy required to partially overcome intermolecular attractive forces in the solid and causing a phase transition to liquid water. The solution remains at 0 °C until all the ice is melted. Only the amount of water existing as ice changes until the ice disappears. Then the temperature of the water can rise.

What feature characterizes the dynamic equilibrium between a liquid and its vapor in a closed container?

Identify two common observations indicating some liquids have sufficient vapor pressures to noticeably evaporate?

We can see the amount of liquid in an open container decrease and we can smell the vapor of some liquids.

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