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Units and Gas Laws

Units and Gas Laws
Dr. MJ Patterson

The trickiest part of working with the gas laws is keeping the units straight.  The gas laws involve 5 different parameters (pressure, volume, amount, R constant and temperature), each with its own set of units.  This page will discuss which units are commonly used for the different variables, conversions between the common units and an approach to make your calculations "unit proof" by using a standard set of units every time.

Volume (V) - Liters

The two most commonly used units for volume are liters and milliliters.  To convert between them, you move the decimal point three places.  Before we look at moving the decimal right or left, let''s look at the size of the units.  A liter is bigger than a milliliter, 1000 times bigger in fact.  So, if a particular volume is expressed in both liters and milliliters, the number of liters should be smaller than the number of milliliters.

As an example, think about a 2 liter soda bottle.  The volume of soda expressed in liters is 2.  But, it takes a lot more milliliters to make up the same volume.  When we move the decimal three places, we should end up with a larger number or 2000 mL.  To double check, compare 2000 and 2.  The number in milliliters is larger than the number in liters.  So, to convert from liters to milliliters, move the decimal 3 places to the right.  To convert from milliliters to liters, move the decimal 3 places to the left.

For the purposes of gas laws, the standard unit for volume is the liter.  To be safe, convert all volumes to liters at the beginning of a problem.

Temperature (T) - Kelvin

All temperatures must be expressed in Kelvin for gas law problems.  There are no exceptions!  Since most thermometers and other temperature measuring devices are calibrated in Celcius, we need to convert the temperatures from Celcius to Kelvin.   This time, the conversion is performed by addition or subtraction.

K = oC + 273
oC = K - 273

Notice that the unit Kelvin is abbreviated just with the letter K - no degree sign.

For the purposes of gas laws, the standard unit for temperature is the Kelvin.  To be safe, convert all temperatures to Kelvin at the beginning of a problem.

Pressure (P) - Atmospheres

The two most common pressure units are atmospheres and torr (or mm Hg - read millimeters of mercury).  One atmosphere is defined to be the atmospheric pressure exerted at sea level on a clear sunny day.  At this pressure, a straight tube sealed on one end that has been filled with mercury and upended in a pool of mercury will support a column of mercury that is 760 mm tall.  At this height, the force of gravity pulling the mercury down in the tube is counterbalanced by the force of the atmosphere pushing down on the pool of mercury and forcing some mercury up into the tube.  Of course, the unit of mm Hg is too straightforward for scientists, so someone renamed the unit in honor of an early scientist who performed experiments with gases - Evangelista Torricelli.  And, now we use both names interchangeably to confuse students.

The relevant conversion factors are:

1 atm = 760 mm Hg = 760 torr

To convert from torr to atmospheres, divide by 760.  To convert from atmospheres back to torr, multiply by 760.  To convert between torr and mm Hg, leave the number alone and just write the other unit.

(To confuse matters further, when meteorologists report the current pressure, they use units of inches of mercury!)

For the purposes of gas laws, the standard unit for pressure is the atmosphere.  To be safe, convert all pressures to atmospheres at the beginning of a problem.

Amount (n) - Moles

For the purposes of stoichiometry, the mole is the best unit to express the amount of a chemical because it is so central to conversions.  In laboratory work, however, we use a balance to determine the amount of a chemical in grams.  Without peeking below, what is the conversion factor between grams and moles?

Molecular weight!  This needs to be tattooed on the backs of your eyelids by now.  Conversion factor:

1 mole of chemical = MW in g of chemical

To convert from grams to moles, divide by the MW.  To convert from moles to grams, multiply by the MW.

For the purposes of gas laws, the standard unit for amount is the mole.  To be safe, convert all amounts to moles at the beginning of a problem.

Ideal Gas Constant (R) - 0.0821 liter atm / (mol K)

The value used for the ideal gas constant is what forces us to use a standard set of units in gas law calculations.  If R appears in an equation, and you use 0.0821 liter atm / (mol K) as the value and units, then your volume must be in liters, pressure in atms, amount in moles and temperature in Kelvin in order for the units to cancel.  If you use different units for any of these variables, then you must use a different numerical value for R.  Consequently, there are two approaches to consider.  In the first, you can memorize different values for R in all sorts of different units and never worry about unit conversions.  In the second, you can memorize one value for R, and convert all of your variables into that set of units.  I prefer the second approach, and that is what I have been pushing in this page.

You need to memorize this value for R.  It will not be provided on the exam.  R = 0.0821 liter atm / (mol K)

For the purposes of gas laws, the standard value for R is 0.0821 liter atm / (mol K).

Summary:

The following comprise our standard set of units for gas laws:

P in atmospheres
V in liters
n in moles
R in 0.0821 liter atm / (mol K)
T in Kelvin