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# Conversions between Moles and Gas Volume

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How can you tell how much gas is in these containers?

Small gas tanks are often used to supply gases for chemistry reactions.  A gas gauge will give some information about how much is in the tank, but quantitative estimates are needed so the reaction will be able to proceed to completion.  Knowing how to calculate needed parameters for gases is very helpful to avoid running out too early.

### Conversions Between Moles and Gas Volume

Molar volume at STP can be used to convert from moles to gas volume and from gas volume to moles.  The equality of 1 mole = 22.4 L is the basis for the conversion factor.

#### Sample Problem One: Converting Gas Volume to Moles

Many metals react with acids to produce hydrogen gas.  A certain reaction produces 86.5 L of hydrogen gas at STP.  How many moles of hydrogen were produced?

Step 1: List the known quantities and plan the problem.

Known

• 86.5 L H 2
• 1 mol = 22.4 L

Unknown

• moles of H 2

Apply a conversion factor to convert from liters to moles.

Step 2: Calculate.

$86.5 \ \text{L H}_2 \times \frac{1 \ \text{mol H}_2}{22.4 \ \text{L H}_2}=3.86 \ \text{mol H}_2$

The volume of gas produced is nearly four times larger than the molar volume.  The fact that the gas is hydrogen plays no role in the calculation.

#### Sample Problem Two: Converting Moles to Gas Volume

What volume does 4.96 moles of O 2 occupy at STP?

Step 1: List the known quantities and plan the problem.

Known

• 4.96 moles O 2
• 1 mol = 22.4 L

Unknown

• volume of O 2

Step 2:  Calculate.

$4.96 \ \text{moles} \times \ \ {22.4 \ \text{liters/mole}}=111.1 \ \text{liters}$

The volume seems correct given the number of moles.

#### Sample Problem Three: Converting Volume to Mass

If we know the volume of a gas sample at STP, we can determine how much mass is present.  Assume we have 867 liters of N 2 at STP.  What is the mass of the nitrogen gas?

Step 1: List the known quantities and plan the problem.

Known

• 867 L N 2
• 1 mol = 22.4 L
• molar mass of N 2 = 28.02 g/mol

Unknown

• mass of N 2

Step 2: Calculate.

We start by determining the number of moles of gas present. We know that 22.4 liters of a gas at STP equals one mole, so:

$867 \ \text{litres} \times \frac{1 \ \text{mole}}{22.4 \ \text{liters}}=3.87 \ \text{moles}$

We also know the molecular weight of N 2 (28.0 grams/mole), so we can then calculate the weight of nitrogen gas in 867 liters:

$38.7 \ \text{moles} \times \frac{28 \ \text{grams}}{\text{mole}}=1083.6 \ \text{grams N}_2$

In a multi-step problem, be sure that the units check.

#### Summary

• Conversions between moles and volume of a gas are shown.

#### Practice

Work the practice problems at the link below. Focus on conversions between volume and moles, but try some of the others:

#### Review

1. Why do the gases need to be at STP?
2. When does the identity of the gas become important?