Professor Dave here, let’s check the pressure.
We used to think that air was just empty space, but in the modern age, we know that air contains
matter.
Specifically, molecules of nitrogen, oxygen, and many others.
These molecules participate in collisions where they transfer some of their kinetic
energy onto whatever they collide with.
This means that air exerts pressure on its surroundings, and we are able to measure this
pressure.
Atmospheric pressure decreases with altitude, because fewer and fewer molecules have enough
kinetic energy to go against gravity to get farther and farther away from the Earth, resulting
in an atmosphere that thins as we go.
For this reason, it will be useful to be able to quantify atmospheric pressure.
One method of measuring atmospheric pressure is by using something called a barometer.
A barometer is a glass tube that is closed at one end and then filled with a liquid like
mercury, that is chosen specifically because it is nonvolatile, which means it does not
evaporate, but will remain a liquid.
The tube is then inverted and placed into a container of that liquid.
The atmosphere exerts pressure on the liquid when particles from the atmosphere collide
with particles in the liquid.
This activity keeps the liquid in the tube at a particular height, so by observing the
height of the column of liquid in the tube, we can see how much the atmosphere is pushing
down on the liquid, and in doing so, we are measuring atmospheric pressure.
In terms of the liquid chosen, if we were to use water, normal atmospheric pressure
can support a column of water over 10 meters tall, which is not terribly convenient for
storing or taking measurements.
For this reason, we decided to use a different liquid.
Mercury is much more dense than water, so a mercury barometer will not have to be so tall.
In fact, atmospheric pressure will support a column of mercury that is only 760 millimeters
tall, and this relationship between the height of a column of mercury in a barometer and
atmospheric pressure is where we get the conversion between atmospheres and millimeters of mercury,
as units of pressure.
The pressure exerted by a fluid due to gravity is called hydrostatic pressure, which is represented
by p, and is equal to the height of the fluid, times the density of the fluid, times g, the
acceleration due to gravity.
In order to support a column of fluid of a particular height, the atmospheric pressure
will have to equal the hydrostatic pressure.
We can see that this equation will accurately predict the atmospheric pressure necessary
to support a column of mercury of a particular height if we plug in some known values.
For example, let’s calculate the atmospheric pressure required to support a column of mercury
with a height of 760 millimeters.
The density of mercury is 13.6 grams per centimeter cubed, and the acceleration due to gravity
on earth is 9.81 meters per seconds squared, so let’s solve for p.
We will want all our units to agree, so we can plug in the height of the column, and
convert to meters, then the density, converting to kilograms per cubic meter, and then the
gravitational acceleration, which as we said is in meters over seconds squared.
We will get about 101,000 pascals, which is roughly equal to atmospheric pressure, and
therefore corroborates our experimental observation.
There is a device that is similar to a barometer, and it is used to measure not atmospheric
pressure, but rather the pressure exerted by a gas that is trapped in a container.
This is called a manometer.
In a manometer, there will be a bulb containing some gas.
This connects to a U-shaped tube that will contain some nonvolatile liquid, like mercury,
and the gas particles in the bulb will push down on the liquid just the way atmospheric
particles push down on the liquid in a barometer.
This tube can be closed to the atmosphere, in which case the difference in height between
the two arms of the liquid will be equal to the pressure of the gas.
This is called a closed-end manometer.
There can also be open-end manometers, in which the top of the tube is open to the atmosphere.
In this case, the height of the two arms of the liquid will depend on both the pressure
of the gas and atmospheric pressure, and the difference in height will be equal to the
difference in the two pressures, the one in the bulb and the one outside of the apparatus.
We may have to add the height difference to atmospheric pressure or subtract it from atmospheric
pressure, depending on which arm is taller, as the gas may be pushing with more force,
or the atmosphere may be pushing with more force.
Let’s say we are looking at a closed-end manometer filled with mercury, and we measure
the difference in height as being 26.4 centimeters.
We can use this value to express the pressure of the gas that is pushing down on the mercury
in a few different units.
If we want to use torr, we can just take our value in centimeters of mercury and convert
into millimeters of mercury, which we will treat as being equivalent to torr.
From torr, we could convert into atmospheres, pascals, or bar.
So just by measuring the difference in height of the arms of liquid mercury, we can state
in a quantitative way, precisely the amount of pressure that a sample of gas exerts in
relevant units.
Let’s say instead we are looking at an open-end manometer.
Here, we measure the difference in height as being 13.7 centimeters.
Assuming this is taking place at sea level, what is the pressure of the gas?
This time, we have to utilize atmospheric pressure.
If the mercury rises higher on the right side, that means that the gas is pushing on it with
more pressure than the atmosphere is.
So the difference in height of the two arms must be added to atmospheric pressure to get
the pressure of the gas.
We know atmospheric pressure is 760 millimeters of mercury, so we will take the 137 measured
here and add it to 760 to get 897 millimeters mercury.
From there, we could convert into any other unit of pressure if we wished.
These kinds of devices have an extremely practical application, and that involves measuring the
pressure exerted by a gas that is evolving from a chemical reaction.
Plotting this pressure over time allows us to do kinetic studies on any reaction that
evolves a gaseous product.
So between barometers and manometers, we now have a variety of ways to measure the pressure
exerted by the atmosphere, or an isolated sample of gas.
Let’s check comprehension.