Calculating Gas Volumes

Avogadro’s Law

Avogadro’s Law states that at a constant temperature and pressure, equal amounts of different gases occupy the same volume of space. In other words, gases with the same amount in moles will take up the same amount of space.

To better understand this concept, it’s helpful to define the molar gas volume. One mole of any gas, at room temperature and pressure (RTP), occupies a volume of 24 dm³ (24,000 cm³). This value is constant for all gases at RTP.

The triangle below shows the relationship between volume, the amount of gas (in moles) and the molar gas volume (24 dm³).

The image displays a triangle divided into three sections. At the top section of the triangle, the word "Volume" is written, followed by the unit "(dm³)" below it. The bottom left section of the triangle has the text "Amount of gas (moles)", and the bottom right section contains the value "24 dm³". The sections are delineated by blue lines, and the overall design represents the relationship between the volume and the amount of gas in moles.

By understanding the relationship between these variables, we can make predictions about how changes in one variable will affect the others.

Calculating Volume

To calculate the volume of a known amount of gas, you can use the following equation:

Volume (dm³) = Number of moles × Molar volume (dm³)

Let’s work through an example to see how this equation can be used.

Example

Calculate the volume of 68 g of ammonia gas (NH3), at room temperature and pressure. Molar volume = 24 dm³

To begin, we need to find the amount of ammonia gas in moles. To do this, we use the formula:

Amount in mol = Mass (g) ÷ Relative atomic mass

The relative formula mass of NH3 is 17, where 14 is for Nitrogen and 1 is for each of the three Hydrogen atoms (14 + 1 + 1 + 1). Therefore:

Amount in mol = 68 ÷ 17 = 4

Now that we know the amount of ammonia gas in moles, we can use the equation for volume:

Volume (dm³) = Number of moles × 24

= 4 × 24

Volume (dm3) = 96 dm3

Therefore, the volume of 68 g of ammonia gas (NH3), at room temperature and pressure, is 96 dm³.


Calculating the Number of Moles

To calculate the amount of a known volume of gas, you can use the following equation:

Amount in mol = Volume (dm³) ÷ Molar volume (dm³)

Let’s work through an example to see how this equation can be used.

Example

Calculate the amount of sulfur dioxide that occupies 480 cm³ at room temperature and pressure. Molar volume = 24,000 cm³

We can use the equation for the amount in mol:

Amount in mol = Volume (dm³) ÷ Molar volume (dm³)

Substituting in the values, we get:

Amount in mol = 0.48 ÷ 24 = 0.02 mol

Therefore, the amount of sulfur dioxide that occupies 480 cm³ at room temperature and pressure is 0.02 mol.


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