The Ideal Gas Law Video Lessons

Concept: Boyle's Law

# Problem: An "empty" container is not really empty if it contains air. How may moles of nitrogen are in an "empty" two-liter cola bottle at atmospheric pressure and room temperature (25 °C)? Assume ideal behavior.Express your answer to three significant figures and include the appropriate units.The ideal gas law, PV = nRT is independent of the kind of gas. In other words, the pressure exerted by a given number of ideal gas particles is the same whether the sample consists of all one type of particle or a mixture of different kinds of particles.Therefore, the pressure exerted by a mixture of gases can be expressed as follows:Ptotal=(n1+n2+n3+...)RTV=ntotalRTVA partial pressure is the pressure exerted by just one type of gas in a mixture. A partial pressure is calculated using only the number of moles of that particular gas, instead of the total number of moles:P1=n1RTV, P2=n2RTV, P3=n3RTV, etc.The sum of the partial pressures is equal to the total pressure in the mixture:Ptotal=P1+P2+P3+...Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules.

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###### Problem Details

An "empty" container is not really empty if it contains air. How may moles of nitrogen are in an "empty" two-liter cola bottle at atmospheric pressure and room temperature (25 °C)? Assume ideal behavior.

Express your answer to three significant figures and include the appropriate units.

The ideal gas law, PV = nRT is independent of the kind of gas. In other words, the pressure exerted by a given number of ideal gas particles is the same whether the sample consists of all one type of particle or a mixture of different kinds of particles.

Therefore, the pressure exerted by a mixture of gases can be expressed as follows:

${\mathbf{P}}_{\mathbf{total}}\mathbf{=}\frac{\left({n}_{1}+{n}_{2}+{n}_{3}+...\right)\mathbf{RT}}{\mathbf{V}}\mathbf{=}\frac{{\mathbf{n}}_{\mathbf{total}}\mathbf{RT}}{\mathbf{V}}$

A partial pressure is the pressure exerted by just one type of gas in a mixture. A partial pressure is calculated using only the number of moles of that particular gas, instead of the total number of moles:

The sum of the partial pressures is equal to the total pressure in the mixture:

${\mathbf{P}}_{\mathbf{total}}\mathbf{=}{\mathbf{P}}_{\mathbf{1}}\mathbf{+}{\mathbf{P}}_{\mathbf{2}}\mathbf{+}{\mathbf{P}}_{\mathbf{3}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}$

Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules.