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50 KMT P, T, & V

By Tamara Hyde
Last updated almost 4 years ago
16 Questions
This unit is on gas laws. When dealing with gases, there are 3 variables which are highly important. They are interconnected. This means that you cannot change one without significantly affecting at least one of the others. We will be looking at these three variables in this lesson, and explaining them from a molecular level with the application of the Kinetic-Molecular Theory.

The Kinetic-Molecular Theory has five postulates which need to be understood before you begin to try and understand the variables.

As you read through the five postulates below, be prepared to answer the following 2 questions:
  1. How do particles cause pressure?
  2. What are you really measuring when you measure the temperature of an object?
The kinetic molecular theory (KMT) is a simple microscopic model that effectively explains the gas laws described in previous modules of this chapter. This theory is based on the following five postulates described here. (Note: The term “molecule” will be used to refer to the individual chemical species that compose the gas, although some gases are composed of atomic species, for example, the noble gases.)
  1. Gases are composed of molecules that are in continuous motion, travelling in straight lines and changing direction only when they collide with other molecules or with the walls of a container.
  2. The molecules composing the gas are negligibly small compared to the distances between them.
  3. The pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls.
  4. Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic (do not involve a loss of energy).
  5. The average kinetic energy of the gas molecules is proportional to the kelvin temperature of the gas.

How do particles cause pressure?

What are you really measuring when you measure the temperature of an object?

Hopefully, you can see that the answers have something to do with the fact that gas particles can move more or less freely, bouncing off of each other and off the walls of the container. This is what causes pressure - the collisions of the gas particles with objects. The more collisions there are, the higher the pressure. The harder the collisions, the higher the pressure. This leads to temperature, which is really just a measure of the speed of the particles. When objects heat up, they have more kinetic energy and they move faster. When they cool down they have less kinetic energy, and they move slower.
These are ALL interconnected!!!
If the temperature of a gas is raised, would that affect the pressure?
Yes. It would go up - the KMT can explain why.
If the temperature of a gas is raised, would that affect the volume?
Yes, the particles move faster, so they would need more spread out, taking up more volume.
If the volume of a gas is increased, would that affect the pressure?
Yes, there would be less pressure because the particles would be more spread out and there would be fewer collisions with the walls.

So let's learn about these variables.
Pressure
Units of pressures- 1 atm = 760 mmHg = 760 torr = 101.3 kPa = 14.7 psi
Background:
Pressure is defined as Force / Area such as pounds per square inch (psi). The weight of air pushing down per square inch is 14.7 pounds per square inch or 14.7 psi.

A barometer can be used to measure pressure. A column of mercury (Hg) that is 0.760 meter (760 mm) tall has the same weight as a column of air from sea level to the edge of the stratosphere. The height of this column is a good measure of air pressure… 760 mmHg.

Evangelista Torricelli did a lot of experiments with pressure and so 1 mmHg is also called 1 torr. So, air pressure has a value of 760 torr. This amount of pressure is also called 1 atm (one atmosphere) because it IS the atmosphere.

In metric units, pressure if Newtons (force) per square meter (area). One Newton is not very much pressure… about the weight of a small apple (get it… apple… Newton)… and if that force is exerted over a square meter, the amount of pressure is very small and called a pascal (Pa). It is more useful to talk of kilopascals (kPa) which would be the weight of 1000 small apples exerted over a square meter. Air pressure is equal to 101.3 kPa.
Since each of these values (see the top of the page) represent the same amount of pressure, any two of them can be used as a conversion factor. You can convert one pressure unit into another.

760 torr = ? atm

1atm = ? kPa

745 mmHg into psi

727 mmhg into kPa

52.5 kPa into atm

0.729 atm into mmHg

Temperature
Here is an excerpt from the textbook:
As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved. Since the kelvin temperature scale is absolute, a degree symbol is not included in the unit abbreviation, K. The early 19th-century discovery of the relationship between a gas’s volume and temperature suggested that the volume of a gas would be zero at −273.15 °C. In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this text’s chapter on gases).
The freezing temperature of water on this scale is 273.15 K and its boiling temperature is 373.15 K. Notice the numerical difference in these two reference temperatures is 100, the same as for the Celsius scale, and so the linear relation between these two temperature scales will exhibit a slope of 1K/°C. Following the same approach, the equations for converting between the kelvin and Celsius temperature scales are derived to be:
Tk = Tc + 273
Tc = Tk - 273
So converting between Kelvin (K) and Celsius (oC) is really just a matter of adding or subtracting 273.

894 K = ? oC

25 oC = ? K

1255 K = ? oC

0 oC = ? K

Volume
Volume should be relatively easy. You just need to know how to convert between mL and L. This can be done by moving the decimal according to the KHDbdcm chart or using conversion factors.

25 mL = ?L

822 mL = ?L

7.3 L = ? mL

99 L = ? mL