1. Avogadro Constant Example
2. Avogadro Number Example
3. Avogadro Exam
4. Avogadro Software Examples
5. Avogadro's Number Example Problems
6. Avogadro's Law Equation Example

Avogadro’s number is the number of molecules of gas in a mole. This number is huge, the current figure being 6.022 x 10 23. The unit for Avogadro’s number is mol -1. This means that the measure of the entity in question is per mole. If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro's Law. Adding gas to a rigid container makes the pressure increase. 1 A balloon has been filled to a volume of 1.90 L with 0.0920 mol of helium gas.

Avogadro’s Law Examples in Real Life Avogadro’s law tells about the relationship between the volume of a gas and the number of molecules possessed by it. It was formulated by an Italian scientist Amedeo Avogadro in the year 1811.

Question: Three balloons are filled with different amounts of an ideal gas. One balloon is filled with 3 moles of the ideal gas, filling the balloon to 30 L.

a) One balloon contains 2 moles of gas. What is the volume of the balloon?

b) One balloon encloses a volume of 45 L. How many moles of gas are in the balloon?

Answer:

Avogadro’s law says the volume (V) is directly proportional to the number of molecules of gas (n) at the same temperature.

n ∝ V

This means the ratio of n to V is equal to a constant value.

Since this constant never changes, the ratio will always be true for different amounts of gas and volumes.

where
ni = initial number of molecules
Vi = initial volume
nf = final number of molecules
Vf = final volume. Chrome os with play store download.

Part a) One balloon has 3 moles of gas in 30 L. The other has 2 moles in an unknown volume. Plug these values into the above ratio:

Solve for Vf

(3 mol)Vf = (30 L)(2 mol)
(3 mol)Vf = 60 L⋅mol
Vf = 20 L

You would expect less gas to take up a smaller volume. In this case, 2 moles of gas only took up 20 L.

Part b) This time, the other balloon has a known volume of 45 L and an unknown number of moles. Start with the same ratio as before:

Use the same known values as in part a, but use 45 L for Vf.

Solve for nf

(3 mol)(45 L) = (30L)nf
135 mol⋅L = (30L)nf
nf = 4.5 moles

The larger volume means there is more gas in the balloon. In this case, there are 4.5 moles of the ideal gas in the larger balloon.

Avogadro Constant Example

An alternative method would be to use the ratio of the known values. In part a, the known values were the number of moles. There was the second balloon had 2/3 the number of moles so it should have 2/3 of the volume and our final answer is 2/3 the known volume. The same is true of part b. The final volume is 1.5 times larger so it should have 1.5 times as many molecules. 1.5 x 3 = 4.5 which matches our answer. This is a great way to check your work.

Avogadro Number Analogies

Avogado's Number is so large many students have trouble comprehending its size. Consequently, a small sidelight of chemistry instruction has developed for writing analogies to help express how large this number actually is.

Before looking over the following examples, here's a nice YouTube video about the mole and Avogadro's Number. Have fun and please come back to the ChemTeam when you're done exploring.

1) Avogadro's Number compared to the Population of the Earth:

We will take the population of the earth to be six billion (6 x 10⁹ people). We compare to Avogadro's Number like this:

6.022 x 10²³ divided by 6 x 10⁹ = approx. 1 x 10¹⁴

In other words, it would take about 100 trillion Earth populations to sum up to Avogadro's number.

If we were to take a value of 7 billion (approximate population in 2012), it would take about 86 trillion Earth populations to sum up to Avogadro's Number.

2) Avogadro's Number as a Balancing Act:

At the very moment of the Big Bang, you began putting H atoms on a balance and now, 19 billion years later, the balance has reached 1.008 grams. Since you know this to be Avogadro Number of atoms, you stop and decide to calculate how many atoms per second you had to have placed.

1.9 x 10¹⁰ yrs x 365.25 days/yr x 24 hrs/day x 3600 sec/hr = 6.0 x 10¹⁷ seconds to reach one mole

6.022 x 10²³ atoms/mole divided by 6.0 x 10¹⁷ seconds/mole = approx. 1 x 10⁶ atoms/second

So, after placing one million H atoms on a balance every second for 19 billion years, you get Avogadro Number of H atoms (approximately).

3) Avogadro's Number in Outer Space:

If all the matter in the universe were spread evenly throughout the entire universe, there would be approx. 1 x 10¯⁶ nucleons per cm³. We could do several things with that. For example:

a) What volume (in cm³) of space would hold Avogadro Number of nucleons?

6.022 x 10²³ nucleons/mole divided by 1 x 10¯⁶ nucleons/cm³ = 6.022 x 10²⁹ cm³/mole

b) How many Earths would equal this volume of space (take Earth's radius to be 6380 km)?

4) Avogadro Number of Coins:

Take a common coin of your country and stack up 30 of them. Measure the height in cm and divide by 30. You now have the average height of one coin in centimeters.

a) How high in cm is a stack of Avogadro Number of that coin?
b) How many light years is this? (Light travels 3.00 x 10⁸ km per second)
c) How many 'round-trips' is this to the moon? (Go there and back = one round-trip. The Earth-Moon distance (measured center-to-center is a bit more than 384,000 km.)

Another way to express this type of problem: If you placed one mole of pills (coins, etc.) with a diameter of 1.00 cm side by side, how many trips around the Sun's equator can you make?

Solution:

1) Convert diameter of Sun from km to cm:

(1.392 x 10⁶ km x (10⁵ cm / 1 km) = 1.392 x 10¹¹ cm

Avogadro Number Example

I looked up the diameter of the Sun online.

2) Calculate circumference of sun:c = πd

Avogadro Exam

c = (3.14159) (1.392 x 10¹¹ cm)

c = 4.3731 x 10¹¹ cm

3) Calculate trips around the Sun:

Since each pill = 1.00 cm, one mole of them covers 6.022 x 10²³ cm

6.022 x 10²³ cm / 4.3731 x 10¹¹ cm

Avogadro Software Examples

1.377 x 10¹² times around the Sun.

Avogadro's Number Example Problems

5) Avogadro Number of Pieces of Paper:

Avogadro's Law Equation Example

If you had a mole of sheets of paper stacked on top of each other, how many round trips to the Moon could you make? (Hint: a stack of 100 sheets of ordinary printer paper is about 1.0 cm.)

6) The area of the ChemTeam's home state of California is 403932.8 km². Suppose you had 6.022 x 10²³ sheets of paper, each with dimensions 30 cm x 30 cm. (a) How many times could you cover California completely with paper? (b) Suppose each sheet of paper is 1 mm thick. How high would the paper be stacked?

7) If you drove 6.022 x10²³ days at a speed of 100 km/h, how far would you travel?

8) If you spent 6.022 x 10²³ dollars at an average rate of 1.00 dollar/s, how long in years would the money last? (Assume that every year has 365 days.)