Unit 2: Advance Basics

Section 6: Avogadro's Law and the Ideal Gas Law

* Avogadro's Law
o Practice Problems
* Ideal Law
o Practice Problems
o Practice Problems

Avogadro's law

In Unit 1, we told about how Avogadro said that equal volumes of gases at
the same temperature and pressure contain the same number of particles.
Mathematically, this is represented as V = an, where V = volume, n = number
of moles, and a = a proportionality constant. Basically, this equation means
that for a gas at constant temperature and pressure the volume is directly
propotional to the number of moles of gas.

 

Practice Problem:

Suppose we have a sample of oxygen gas, that is 15 L in volume and contains
.75 moles of gas. If all of the oxygen is converted to ozone, at constant
temperature and pressure, what will be the volume of the ozone?

Answers

The balanced equation for the reaction is:

3 O2 + 2 O3. To calculate the moles of ozone produced, we must use the mole
ratio, 2 mol O3 / 3 mol O2. We started out with .75 moles of O2, so we
multiply it by the mole ratio:

.75 mol O2 x 2 mol O3/3 mol O2 = .5 mol O3

Avogadro's law can be rearranged so that V/n = a. Since a is constant, the
equation can be rewritten as:

V1 / n1 = V2/n2.

V1 = 15 L, n1 = .75 mol, n2 = .5 mol, and you must solve for V2. Plugging in
the numbers, (15 L) / (.75 mol) = (V2) / (.5 mol), and V2 = 10 L.

Ideal Gas Law

So far, we have learned of three laws that describe the behavior of gases.
They are Boyle's Law, Charles's Law, and Avogadro's law. These relationships
show how volume of a gas depends on pressure, temperature, and number of
moles present. They can be combined, represented by the equation V =
R([Tn]/P), where R is the combined proportionality constant called the
universal gas constant. When pressure is in atmospheres and volume is in
liters, R has the value of 0.08206 L atm/K mol. The above equation can also
be rearranged to what is known as the ideal gas law, PV = nRT. When using
this equation, remember to convert pressure to atmospheres, volume to
liters, temperature to kelvins, and amount present to moles.

Practice problems:

A sample of oxygen gas has a volume of 4.52 liters at a temperature of 10 oC
and a pressure of 1.5 atm. Calculate the number of moles of oxygen gas
present in this sample.

Answers

The ideal gas law can be rearranged to solve for n (number of moles), n =
PV/RT. In this problem, P = 1.5 atm, V = 4.52 L, T = 10 oC + 273 = 283 oK, and
R = .08206 L atm/K mol. Plugging in your numbers, you have n = (1.5
atm)(4.52 L)/(.08206 L atm/K mol)(283 K) = .292 moles.

Practice Problems

A sample of hydrogen gas has a pressure of 345 torr at a temperature of -10
C and a volume of 4.33 L. If conditions are changed so that the temperature
is 26 C and the pressure is 468 torr, what will be the new volume?

Since the pressure, temperature, and volume all change while the number of
moles remains constant, we rearrange the ideal gas law to PV/T = nR. Since
nR will be the same before and after the change, we can say that:

P1 V1 / T1 = P2 V2 / T2.

We are solving for V2, so we rearrange this to the form:
V2 = T2 P1 V1 / T1 P2. P1 = 345 torr, T1 = -10 oC + 273 = 263 oK, V1 = 4.33 L,
T2 = 26 oC + 273 = 299 oK, P2 = 468 torr, and we have to solve for V2.
Plugging in the numbers, V2 = (299 K)(345 torr)(4.33 L)/(263 K)(468 torr) =
3.63 liters.