Unit 2 Energy_and_States_of_Matter

Energy and States of Matter I

In the last unit we introduced the particle model for matter and used it to explain the law of conservation of mass and density. We will continue to develop this model in this unit.

Diffusion

Diffusion is the spreading out of a substance from areas of high concentration to areas with lower concentration. Examples include the spreading of the odor of ammonia once a bottle is opened. Diffusion occurs more rapidly in gases and slower in liquids. We observed the diffusion of a dye through both hot and cold water. Here are some questions to consider:

Why does diffusion occur more rapidly through a gas than a liquid or solid?
How fast do you think diffusion would occur through a solid?
Why does temperature affect the rate of diffusion through a liquid?

Phases of Matter, Particle Diagrams, and Motion of Particles

One of the reasons for the differences in the rate of diffusion is the arrangement of particles.

In a solid, the particles are tightly packed, resulting in no noticeable diffusion.
In a liquid the particles are only a little farther apart but can move from one point to another allowing for slow diffusion.
In a gas, the particles are very far apart and move very fast, which allows for rapid diffusion.

All states of matter experience some molecular motion. The largest amount of motion is observed in gases and the least amount of motion is observed in solids. Adding more and more energy will increase the temperature, movement and spacing of the particles. If we cool a substance the movement decreases. Can we remove all of the energy from a substance? If so, what happens to the motion of the particles?

Energy

Energy is a hard thing to grasp. Right now, the best we can do is to use a definition developed in the 18th century. Energy was thought of as a substance like quantity that could be transferred from one object to another. This "substance" was named caloric and cannot be created nor destroyed. Energy is responsible for all change. For example, when you kick a soccer ball, energy is transferred from your body to the ball. Another example is when a log burns in a wood stove, it releases its energy and transfers it to the stove and to the surrounding room.

In a population of particles of a substance, there is distribution of energy among the particles. Some particles have greater than average energy, some have lower than average energy, but most have an energy near the average. The graph below shows how energy is distributed among a population of atoms. At higher temperatures, the graph looks similar, but the average energy is greater than at cooler temperatures. We can define temperature as a measure of the average energy of motion (kinetic energy).

Kinetic Molecular Theory

Our view of matter now includes particles and motion. When we add or remove energy, particles of matter speed up or slow down. When substances are solids or liquids, the particles are arranged closer together and are held together by attractions between neighboring particles. In solids, the motion of particles is limited to vibration. The arrangement of liquids allow for vibrations, rotations and some translational motion. In gases, the particles are very far apart and exert no attractions on each other. They exhibit vibrational, rotational and translational motion.

Gases

Gases were among the first substances that were understood by scientists in the 17th century. While its difficult to measure the mass of a gas, it is fairly easy to measure the volume, temperature and pressure of a gas.

Pressure

Pressure exerted by gas molecules within a container is caused by collisions of the molecules with the side of the container. Each collision contributes some force. Pressure is the force exerted per area.

Atmospheric pressure is measured with a barometer. Gas pressure can be measured with one of two kinds of manometers. The more common manometer used is the open manometer.

The difference between air and gas pressure is the difference in the height of the columns of mercury, DP. If the pressure of the gas is less than that of the air, DP is subtracted from the air pressure to calculate the gas pressure. If the pressure of the gas is more than the air DP is added to air pressure to calculate the gas pressure.

Units of Gas Pressure

SI units of pressure are Pascals (Pa), though kilopascals (kPa) are more commonly used. There are several units used for expressing pressure.

101.3 kPa = 1 atm = 760 mm Hg = 760 torr = 14.7 psi

Measurements

While it may not be easy to measure the mass of a gas, we can easily measure volume, temperature and pressure. We can change one variable and measure the effect on another variable. For example:

If a gas is heated in an enclosed container that cannot expand, what happens to the pressure? If the particles speed up, how does that affect the force of each collision with the wall of the container and the collision frequency? If a gas is cooled to 0 C, does it mean that it has no energy? We know that there are temperatures below 0C, so 0 C doesn’t really represent a real zero. When performing calculations with gases, we need to use the Absolute temperature scale, which need to be expressed in units of Kelvins.

T (K) = C + 273

Gas Laws: How are Pressure, Volume, Temperature and Amount Related?

P a T: Pressure is directly proportional to temperature. As temperature increases, pressure increases. As temperature decreases, pressure decreases.

V a T: Volume is directly proportional to temperature. As temperature increases, volume increases. As temperature decreases, volume decreases.

V a 1/P: Volume is inversely proportional to pressure. As pressure increases, volume decreases. As pressure decreases, volume increases

V a n: Volume is directly proportional to amount . As the amount of gas increases, the volume increases. As the amount of gas decreases, the volume decreases.

P a n: pressure is directly proportional to amount . As the amount of gas increases, the pressure increases. As the amount of gas decreases, the pressure decreases.

Solving Gas law problems

We can make predictions of how the volume, temperature or pressure are affected by changing other variables, by organizing our information into a table. The first row includes initial conditions, the second row has final conditions and the third row describes the change on the unknown variable.

Example 1:

25 ml of a gas is collected at 6.0 atm pressure at 27 C (300 K). Calculate the volume at 1 atm and 0 C (273 K).

	P	T	V	n
Initial	6 atm	300 K	25 ml	--
Final	1 atm	273 K	??	--
Effect	decreases volume	decreases volume

From our table we see that both temperature and pressure changes contribute to a decrease in volume. We set our problem up like a conversion, starting with our initial volume. We multiply the volume by the appropriate ratios of temperature and pressure that will produce the changes that we indicated in the change row.

25 ml | 273 K | 6 atm = 136.5 ml
| 300 K | 1 atm

Example 2:

130 ml of a gas is collected at 750 mm Hg pressure at 20 C (293 K) Calculate the volume at 800 mm Hg and 100 C (373 K).

	P	T	V	n
Initial	750 mm Hg	293 K	130 ml	--
Final	800 mm Hg	373 K	??
Effect	decreases volume	increases volume

From our table we see that the temperature change contributes to an increased volume whereas the pressure change contributes to a decrease in volume. We set our problem up like a conversion, starting with our initial volume. We multiply the volume by the appropriate ratios of temperature and pressure that will produce the changes that we indicated in the change row.

130 ml | 373 K | 750 mm Hg = 155.2 ml
| 293 K | 800 mm Hg

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