Molar Volume, Avogadro's Law



The molar volume is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure.

There are two standards, commonly used in schools:

  • STP (standard temperature and pressure) which is 0 ºC and 1 atmosphere.
  • RTP (room temperature and pressure) which is 20 ºC and 1 atmosphere.
In this lesson, we will learn the Molar Volume, Avogadro's Law, how to calculate gas volumes given moles and grams, how to calculate moles given gas volumes and how to calculate gas volumes given the chemical equation.

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Molar Volume

Avogadro’s Law states that:

1 mole of every gas occupies the same volume, at the same temperature and pressure.

At STP (standard temperature and pressure), this volume is 22.4 liters

At RTP (room temperature and pressure), this volume is 24 dm3 (liters)

We can also say:

The molar volume of a gas is 22.4 liters at STP (standard temperature and pressure).

The molar volume of gas is 24 dm3 at RTP (room temperature and pressure).

How to find the molar volume of a gas using the ideal gas law. The most common molar volume is the molar volume of an ideal gas at standard temperature and pressure (273 K and 1.00 atm)



Gas volumes from moles and grams

Example:

Calculate the volume of carbon dioxide gas, CO2, occupied by (a) 5 moles and (b) 0.5 moles of the gas occupied at STP.

Solution:

a) Volume of CO2

= number of moles of CO2 × 22.4 L

= 5 × 22.4

= 112 L

b) Volume of CO2

= number of moles of CO2 × 22.4 L

= 0.5 × 22.4

= 11.2 L

 

The following video shows an example of grams to moles to liters conversion.
It shows how to convert grams of a substance to liters at STP


Moles from Gas Volume

Example:

Calculate the number of moles of ammonia gas, NH3, in a volume of 80 L of the gas measured at STP.

Solution:

Volume of gas = number of moles × 22.414 L/mol

 

The following video shows an example of liters to moles conversion. It shows how to convert lit res of a gas at STP into moles



Gas volumes from equations

From the equation for a reaction, we can tell how many moles of a gas take part. Using Avogadro’s Law, we can also work out its volume.

Example:

What volume of hydrogen will react with 22.4 liters of oxygen to form water? (All volumes are measured at STP)

Solution:

Step 1: Write a balanced equation for the reaction.

2H2 (g) + O2 (g) → 2H2O (l)

Step 2: Calculate the volume.

From the equation, 2 volumes of hydrogen react with 1 of oxygen or

2 × 22.4 liters of hydrogen react with 22.4 liters of oxygen.

The volume of hydrogen that will react is 44.8 liters.


Example:

When sulfur burns in air it forms sulfur dioxide. What volume of this gas is produced when 1 g of sulfur burns? (Ar : S = 32) (All volumes are measured at STP)

Solution:

Step 1: Write a balanced equation for the reaction.

S (s) + O2 (g) → SO2 (g)

Step 2: Get the number of moles from the grams.

32 g of sulfur atoms = 1 mole of sulfur atoms

So, 1 g = 1 ÷ 32 mole or 0.03125 moles of sulfur atoms

1 mole of sulfur atoms gives 1 mole of sulfur dioxide molecules

So, 0.03125 moles of sulfur atoms gives 0.03125 moles of sulfur dioxide

Step 3: Get the volume.

1 mole of sulfur dioxide molecules has a volume of 22.4 at STP

So, 0,03125 moles has a volume of 0.03125 × 22.4 = 0.7 liters at STP

So, 0.7 liters of sulfur dioxide are produced.



Examples and practice problems of solving equation stoichiometry questions with gases. We calculate moles with 22.4 L at STP, and use molar mass (molecular weight) and mole ratios to figure out how many products or reactants we have.




Examples and practice problems of solving equation stoichiometry questions with gases. We calculate moles with the Ideal Gas Law, because the conditions are not at STP, and use molar mass (molecular weight) and mole ratios to figure out how many products or reactants we have.







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