Conversion Of Moles To Liters

10.7: Conversions Between Moles and Gas Volume

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

Pocket-size gas tanks are often used to supply gases for chemical science reactions. A gas gauge will give some information about how much is in the tank, just quantitative estimates are needed and so that the reaction volition exist able to proceed to completion. Knowing how to summate the necessary parameters for gases is very helpful to avoid running out earlier than desired.

Conversions Between Moles and Gas Volume

Molar volume at STP tin be used to convert from moles to gas volume and from gas volume to moles. The equality of \(1 \: \text{mol} = 22.4 \: \text{L}\) is the basis for the conversion factor.

Example \(\PageIndex{one}\): Converting Gas Volume to Moles

Many metals react with acids to produce hydrogen gas. A sure reaction produces \(86.5 \: \text{Fifty}\) of hydrogen gas at STP. How many moles of hydrogen were produced?

Solution

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

Known

\(86.5 \: \text{L} \: \ce{H_2}\)
\(1 \: \text{mol} = 22.4 \: \text{Fifty}\)

Unknown

moles of H₂

Apply a conversion gene to convert from liters to moles.

Footstep 2: Calculate.

\[86.5 \: \text{L} \: \ce{H_2} \times \frac{1 \: \text{mol} \: \ce{H_2}}{22.iv \: \text{L} \: \ce{H_2}} = 3.86 \: \text{mol} \: \ce{H_2}\nonumber \]

Pace 3: Call up near your result.

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

Example \(\PageIndex{two}\): Convertig Moles to Gas Volume

What book does \(4.96 \: \text{mol}\) of \(\ce{O_2}\) occupy at STP?

Solution

Step i: Listing the known quantities and plan the problem.

Known

\(4.96 \: \text{mol} \: \ce{O_2}\)
\(one \: \text{mol} = 22.four \: \text{L}\)

Step 2: Calculate.

\[iv.96 \: \text{mol} \times 22.4 \: \text{Fifty/mol} = 111.1 \: \text{L}\nonumber \]

Footstep 3: Think about your effect.

The book seems correct given the number of moles.

Example \(\PageIndex{iii}\): Converting Book to Mass

If we know the book of a gas sample at STP, nosotros tin can determine how much mass is present. Assume nosotros have \(867 \: \text{50}\) of \(\ce{N_2}\) at STP. What is the mass of the nitrogen gas?

Solution

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

Known

\(867 \: \text{L} \: \ce{N_2}\)
\(1 \: \text{mol} = 22.4 \: \text{L}\)
Molar mass \(\ce{N_2} = 28.02 \: \text{g/mol}\)

Step 2: Calculate.

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

\[867 \: \text{L} \times \frac{ane \: \text{mol}}{22.four \: \text{L}} = 38.seven \: \text{mol}\nonumber \]

We also know the molecular weight of \(\ce{N_2}\) \(\left( 28.0 \: \text{g/mol} \right)\), so nosotros can and then calculate the weight of nitrogen gas in 867 liters:

\[38.vii \: \text{mol} \times \frac{28 \: \text{chiliad}}{1 \: \text{mol}} = 1083.half dozen \: \text{thousand} \: \ce{N_2}\nonumber \]

Step 3: Retrieve about your result.

In a multi-footstep problem, be sure that the units bank check out.

Summary

Conversions between moles and volume of a gas are shown.

Review

In the issues above, why was the gas always at standard temperature and pressure?
A container contains 45.ii L of Northward_ii gas at STP. How many moles of Due north₂ gas are in the container?
If the gas in the previous problem was CH₄ gas at STP instead of Due north₂ gas, then how many moles of CH₄ gas would in that location be?