Unit 2: Advance Basics

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

Avogadro's Law

Practice Problems

Ideal Law

Practice Problems

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 C 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 C + 273 = 283 K, 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 C + 273 = 263 K, V₁ = 4.33 L, T₂ = 26 C + 273 = 299 K, 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.