1.2.1 Conservation of mass during changes of state

The five changes of state

1. A change of state happens when a substance moves between the solid, liquid and gas states, for example when ice turns into liquid water.
2. In every change of state the particles stay exactly the same particles, and only their arrangement and movement change.
3. Melting turns a solid into a liquid, as when a knob of butter becomes a golden liquid in a hot frying pan.
4. Freezing is the reverse of melting and turns a liquid into a solid, as when water in an ice-cube tray becomes ice in the freezer.
5. Evaporation turns a liquid into a gas, as when a puddle on the pavement slowly disappears on a warm afternoon.
6. Condensation is the reverse of evaporation and turns a gas into a liquid, as when water vapour from a hot shower forms droplets on a cold bathroom mirror.
7. Sublimation turns a solid straight into a gas without the substance ever passing through the liquid state.
8. Solid carbon dioxide, known as dry ice, sublimes at $-78{}^{\circ }C$, so a lump of it shrinks away to nothing without ever leaving a puddle.
9. Melting and freezing are opposite processes, and so are evaporation and condensation, so each of these changes can be undone by its partner.

Conservation of mass

1. Mass is a measure of the amount of matter in an object, and it depends on how many particles the object contains and on the mass of each particle.
2. A change of state does not create any new particles, and it does not destroy any of the particles already there.
3. Each particle also keeps exactly the same mass, because a water molecule in ice is identical to a water molecule in liquid water or in steam.
4. The number of particles and the mass of each particle are both unchanged, so the total mass of the substance stays the same.
5. This is conservation of mass, and it holds for melting, freezing, evaporation, condensation and sublimation alike.
6. For example, $200g$ of ice that melts completely gives exactly $200g$ of liquid water.
7. If that water is frozen again, the result is still $200g$ of ice.
8. What can change is the volume, because the spacing between the particles changes when the state changes.
9. Water is an unusual case, since ice takes up slightly more space than the liquid it formed from, which is why a full glass bottle of water can crack in a freezer even though its mass has not changed.

Closed and open systems

1. A system is the object or group of objects you choose to study, such as a flask and the substance inside it.
2. In a closed system, no matter can get in or out, so a balance shows the total mass staying the same while a change of state happens inside.
3. A sealed plastic bag containing ice cubes is a closed system, because the meltwater stays inside the bag.
4. In an open system, matter can cross the boundary of the system, so the mass measured on a balance can go down or up.
5. An uncovered dish of water left on a windowsill loses mass over a few days, because water particles evaporate and drift away into the air of the room.
6. That mass has not been destroyed, since every one of those particles still exists as water vapour in the surrounding air.
7. If the air in the room were included in the system, the total mass would be found to stay constant.
8. A cold can of drink taken out of the fridge gains a little mass in the same way, because water vapour from the air condenses into droplets on its outside surface.
9. That extra mass has come from the air around the can rather than being created.
10. So whenever a measured mass seems to change during a change of state, the explanation is that particles have entered or left the part being weighed.

1.2.2 Physical and chemical changes

Properties of materials

1. Every material has a set of properties that let you identify it and decide what it can be used for.
2. Properties include the density, the melting point, the boiling point, the colour, the hardness and whether the material conducts electricity.
3. Pure water, for example, is colourless, freezes at $0{}^{\circ }C$, boils at $100{}^{\circ }C$ and has a density of $1000{kg/m}^3$.
4. These properties come from the particles the material is made of, so a material keeps its properties for as long as its particles stay the same.
5. Some properties look different in different states, since ice is hard while water flows, but those differences come from how the particles are arranged rather than from a change in the particles themselves.

Physical changes

1. In a physical change, no new substance is made, and the particles of the material stay the same particles.
2. Only the arrangement, spacing or movement of the particles changes.
3. Because the particles are unchanged, reversing the change brings back the original material with all of its original properties.
4. Every change of state is a physical change.
5. Ice that melts into water can be frozen again, and the new ice has the same melting point, density and appearance as the ice you started with.
6. Water that evaporates from a saucepan can be condensed on a cold lid, and the droplets that form are pure water again.
7. Candle wax that melts near the flame runs down the side of the candle and sets again as solid wax with the same melting point.
8. Dissolving is also a physical change, because salt stirred into water can be recovered as solid salt by evaporating the water away.
9. Changing the shape of a material, such as bending a paper clip or squashing a drinks can, is a physical change too, because the metal is still the same metal.

Chemical changes

1. In a chemical change, the atoms of the starting materials are rearranged to make one or more new substances.
2. The new substances have different properties from the materials you started with.
3. Reversing the conditions does not undo a chemical change, so cooling, freezing or drying the products does not bring back the original material.
4. Bread that has been toasted stays brown and crisp after it cools, because the toasting has formed new substances on its surface.
5. Frying an egg turns the runny, see-through egg white into a firm white solid, and letting the egg cool does not make it runny again.
6. Burning a match turns the wood and the chemicals in the match head into ash, smoke and gases, none of which become a match again when they are cooled.
7. Iron that rusts forms a flaky orange-brown solid that is weaker than iron and has quite different properties.
8. Signs that a new substance has formed include a new colour, a gas being given off, a new smell, or a change that cannot be undone by reversing the conditions.
9. Some chemical changes can be undone by carrying out a different chemical reaction, but that is not the same as reversing the conditions as you can for melting or freezing.

Telling the two changes apart

1. The test is to imagine reversing the change and then ask whether the material gets back its original properties.
2. If reversing the change gives back the original material with the same properties, the change is physical.
3. If reversing the conditions leaves a different material with different properties, the change is chemical.
4. How easy or quick the reversal is does not matter, because condensing all the steam from a boiling kettle back into water is awkward, yet boiling is still a physical change.
5. A big change in appearance is not proof of a chemical change either, because ice, liquid water and steam look very different but are all the same substance.

1.2.3 Heating, temperature and changes of state

Energy stored in a system

1. A system is the object or group of objects you are studying, such as a pan of water on a hob.
2. The particles in a system store energy in two ways.
   1. The particles are always moving or vibrating, so they have energy in their kinetic energy stores.
   2. The particles attract one another and are held at certain distances apart, so they also have energy in their potential energy stores.
3. The total kinetic and potential energy of all the particles is the internal energy of the system.
4. Heating transfers energy into a system from something hotter, such as a hob, a flame or an electric heater.
5. That energy goes into the particles, so heating always increases the internal energy of the system.
6. The extra energy then has one of two effects: it either raises the temperature of the system or produces a change of state.
7. Cooling works the other way round, because energy leaves the system, its internal energy decreases, and the substance either falls in temperature or changes state.

Raising the temperature

1. When a substance is heated and is not changing state, the energy transferred goes mainly into the kinetic energy stores of its particles.
2. The particles then move faster, so the average kinetic energy of the particles goes up.
3. Temperature depends on the average kinetic energy of the particles, so a higher average kinetic energy means a higher temperature.
4. In a solid, heating makes the particles vibrate faster and further about their fixed positions.
5. In a liquid, heating makes the particles slide past one another more quickly.
6. In a gas, heating makes the particles travel faster in random directions and collide more often.

Producing a change of state

1. When a solid reaches its melting point, further heating stops raising its temperature and makes the solid melt instead.
2. During melting, the energy transferred goes into the potential energy stores of the particles rather than their kinetic energy stores.
3. This energy is used to overcome the forces of attraction that hold the particles in fixed positions, so the particles break out of their regular pattern and can move past one another.
4. The average kinetic energy of the particles does not change, so the temperature stays constant until all of the solid has melted.
5. Pure ice melts at $0{}^{\circ }C$, and a glass of iced water stays at about $0{}^{\circ }C$ until every piece of ice has gone, even though it is taking in energy from the warm room.
6. When a liquid reaches its boiling point, further heating makes it boil, and the energy is used to pull the particles completely apart so that they escape as a gas.
7. Water boils at $100{}^{\circ }C$ at normal atmospheric pressure, and a pan of boiling pasta water stays at $100{}^{\circ }C$ however high the hob is turned up, with the extra energy making it boil away faster.
8. Once the change of state is complete, the energy goes back into the kinetic energy stores of the particles and the temperature starts to rise again.
9. The same idea works in reverse, because a liquid that is freezing or a gas that is condensing gives out energy while its temperature stays constant.
10. The internal energy of a system therefore goes up during melting and boiling, even though its temperature does not.

Heating curves

1. A heating curve shows how the temperature of a substance changes with time when it is heated at a steady rate.
2. Temperature goes on the vertical axis in ${}^{\circ }C$, and time goes on the horizontal axis in $s$ or $min$.
3. For ice taken from a freezer at $-18{}^{\circ }C$ and heated steadily, the graph has four main sections.
   1. The line first slopes upwards as the solid ice warms from $-18{}^{\circ }C$ to $0{}^{\circ }C$.
   2. The line then runs flat at $0{}^{\circ }C$ while the ice melts, with solid and liquid present together.
   3. The line slopes upwards again as the liquid water warms from $0{}^{\circ }C$ to $100{}^{\circ }C$.
   4. The line runs flat a second time at $100{}^{\circ }C$ while the water boils and turns into steam.
4. The flat sections show where the substance is changing state, and the sloping sections show where its temperature is rising in a single state.
5. The flat section for boiling lasts much longer than the one for melting, because separating the particles completely to form a gas takes far more energy than loosening them to form a liquid.
6. A cooling curve is the mirror image, with a flat section at the boiling point while the gas condenses and another at the melting point while the liquid freezes.

1.2.4 Specific heat capacity and specific latent heat

Specific heat capacity

1. Different materials need different amounts of energy to warm up by the same number of degrees.
2. The specific heat capacity of a material is the energy needed to raise the temperature of $1kg$ of it by $1{}^{\circ }C$.
3. Its symbol is $c$, and its unit is the joule per kilogram per degree Celsius, $J/kg{}^{\circ }C$.
4. Water has a specific heat capacity of about $4200J/kg{}^{\circ }C$, so $4200J$ is needed to warm $1kg$ of water by just $1{}^{\circ }C$.
5. Aluminium has a specific heat capacity of about $900J/kg{}^{\circ }C$ and copper about $390J/kg{}^{\circ }C$, so the same energy warms $1kg$ of copper by more than ten times as much as $1kg$ of water.
6. A material with a high specific heat capacity warms up slowly and cools down slowly, because it must gain or lose a lot of energy for each degree of temperature change.
7. A material with a low specific heat capacity warms up and cools down quickly.
8. On a sunny day at the beach, the dry sand becomes too hot to walk on barefoot while the sea stays cool, partly because sand has a much lower specific heat capacity than water.
9. Central heating systems pump hot water round the radiators because each kilogram of water carries a large amount of energy from the boiler to the rooms.
10. Specific heat capacity applies only while a substance stays in the same state, because the temperature does not change at all while the state is changing.

Specific latent heat

1. During a change of state, energy is transferred to or from a substance while its temperature stays constant.
2. That energy goes into or comes out of the potential energy stores of the particles as they move apart or closer together, rather than changing their kinetic energy.
3. The specific latent heat of a substance is the energy needed to change the state of $1kg$ of it without changing its temperature.
4. Its symbol is $L$, and its unit is the joule per kilogram, $J/kg$.
5. There is no degree Celsius in the unit, because the temperature does not change during a change of state.
6. The specific latent heat of fusion applies when a substance melts or freezes.
7. The specific latent heat of vaporisation applies when a substance boils or condenses.
8. For water, the specific latent heat of fusion is about $3.34\times 10^{5}J/kg$ and the specific latent heat of vaporisation is about $2.26\times 10^{6}J/kg$.
9. The value for vaporisation is almost seven times larger, because turning a liquid into a gas means pulling the particles completely apart, whereas melting only frees them from their fixed positions.
10. The energy taken in when $1kg$ of a substance melts is given out again when $1kg$ of it freezes, and the same is true for boiling and condensing.
11. This is why a scald from steam at $100{}^{\circ }C$ is much worse than one from water at the same temperature, since the steam releases its latent heat of vaporisation as it condenses on the skin.

Comparing the two quantities

1. Both quantities describe the energy needed per kilogram of a substance, but they describe different things happening to it.
2. Specific heat capacity is about a change in temperature with no change of state.
3. Specific latent heat is about a change of state with no change in temperature.
4. During a temperature change, the energy transferred mainly increases the kinetic energy of the particles.
5. During a change of state, the energy transferred increases the potential energy of the particles.
6. The unit of specific heat capacity is $J/kg{}^{\circ }C$, while the unit of specific latent heat is $J/kg$.
7. On a heating curve, specific heat capacity decides how steep the sloping sections are, and specific latent heat decides how long the flat sections last.

1.2.5 Internal energy and temperature change

What decides the energy needed

1. When a material is heated and stays in the same state, the energy transferred increases its internal energy and raises its temperature.
2. The energy needed for this depends on three things: the mass of the material, its specific heat capacity and the change in temperature.
3. Doubling the mass doubles the energy needed, because there are twice as many particles to speed up.
4. Doubling the temperature rise doubles the energy needed, because each particle has to gain twice as much kinetic energy.
5. A material with double the specific heat capacity needs double the energy for the same mass and the same temperature rise.
6. A kettle filled to the top takes several times longer to boil than one holding just enough water for a single mug, because the energy needed is proportional to the mass of water.

The equation

1. The three factors combine into one equation: $change\; in\; thermal\; energy=mass\times specific\; heat\; capacity\times change\; in\; temperature$.
2. In symbols, this is $\Delta E=mc\Delta \theta$.
   1. $\Delta E$ is the change in thermal energy in joules, $J$.
   2. $m$ is the mass in kilograms, $kg$.
   3. $c$ is the specific heat capacity in $J/kg{}^{\circ }C$.
   4. $\Delta \theta$ is the change in temperature in ${}^{\circ }C$, where $\theta$ is the Greek letter theta.
3. The symbol $\Delta$ means change in, so $\Delta \theta$ is always worked out as the final temperature minus the starting temperature.
4. You do not have to recall this equation from memory, but you must be able to choose it from a list of equations and apply it correctly.
5. The equation applies only when there is no change of state, because the temperature does not change while a substance is melting or boiling.

Calculating the energy change

1. Start by writing the equation, then work out $\Delta \theta$ if the question gives a starting and a final temperature.
2. Convert the mass into kilograms, remembering that $1kg=1000g$.
3. Substitute the values, calculate, and finish with the unit, which for energy is the joule, $J$.
4. Large answers can be written in standard form or in kilojoules, where $1kJ=1000J$.
5. When a material cools down, $\Delta \theta$ is negative and so $\Delta E$ comes out negative, which shows that the internal energy has decreased as energy is transferred to the surroundings.

Rearranging the equation

1. Questions can give you the energy and ask for one of the other quantities instead.
2. To find the specific heat capacity, divide both sides by $m\Delta \theta$ to give $c=\frac{\Delta E}{m\Delta \theta }$.
3. To find the mass, divide both sides by $c\Delta \theta$ to give $m=\frac{\Delta E}{c\Delta \theta }$.
4. To find the temperature change, divide both sides by $mc$ to give $\Delta \theta =\frac{\Delta E}{mc}$.
5. If the question asks for a final temperature, find $\Delta \theta$ first and then add it to the starting temperature, or subtract it if the material is cooling.
6. In a calculation with several steps, keep the unrounded value in your calculator and round only the final answer, usually to the same number of significant figures as the data.

1.2.6 Energy transfer during a change of state

Energy and changes of state

1. While a substance changes state, energy is transferred to or from it but its temperature stays the same.
2. This energy is called latent heat, from a Latin word meaning hidden, because a thermometer shows no sign of it.
3. When a substance melts or boils, it takes in energy, and that energy goes into the potential energy stores of the particles as they move further apart.
4. When a substance freezes or condenses, it gives out the same amount of energy as the particles move closer together again.
5. The energy involved depends on the mass that changes state and on the specific latent heat of the substance.
6. Twice the mass of ice needs twice the energy to melt, which is why a large bag of ice keeps a cool box cold for longer than a handful of cubes.

The equation

1. The equation is $thermal\; energy\; for\; a\; change\; in\; state=mass\times specific\; latent\; heat$.
2. In symbols, this is $E=mL$.
   1. $E$ is the energy transferred in joules, $J$.
   2. $m$ is the mass that changes state in kilograms, $kg$.
   3. $L$ is the specific latent heat in joules per kilogram, $J/kg$.
3. Use the specific latent heat of fusion for melting or freezing, and the specific latent heat of vaporisation for boiling or condensing.
4. There is no temperature in the equation, because the temperature does not change while the state is changing.
5. The mass must be the mass that changes state, so if only part of a block of ice melts, you use only the mass that melts.
6. You do not have to recall this equation from memory, but you must be able to choose it from a list of equations and apply it correctly.
7. Rearranging gives $L=\frac{E}{m}$ for the specific latent heat and $m=\frac{E}{L}$ for the mass.

Calculating the energy

1. Write the equation, convert any mass in grams into kilograms, substitute the values, and give the answer with its unit.
2. Values of specific latent heat are large, so they are usually given in standard form, such as $3.34\times 10^{5}J/kg$.
3. Enter standard form into your calculator with the $\times 10^x$ key rather than typing out the zeros, which avoids slipping a digit.
4. Some questions combine both kinds of energy change, with a substance first warming up to its melting or boiling point and then changing state.
5. For these, work out each stage separately, using $\Delta E=mc\Delta \theta$ for warming and $E=mL$ for changing state, and then add the energies together.