The Law of Partial Pressures, formulated by John Dalton in the early 1800s, is a fundamental principle for understanding gas mixtures. It states that when non-chemically reacting gases are combined, the total pressure exerted by the mixture is the sum of the pressures that each individual gas would exert alone. This law assumes that gas molecules act independently of one another, allowing their individual effects to be combined linearly.
Defining the Law of Partial Pressures
The core concept of Dalton’s Law is partial pressure: the pressure a single gas would exert if it occupied the entire volume of the container by itself. In a mixture, molecules of each gas move randomly and collide with the container walls, creating pressure.
Each gas exerts its own pressure, unaffected by the presence of others. This independence occurs because gas molecules are widely spaced, meaning they rarely interact. They behave essentially as if they were the only gas present.
The validity of Dalton’s Law hinges on the gases not undergoing chemical reactions with each other. If the gases reacted, the number of molecules and their composition would change, invalidating the simple additive pressure calculation. Since all gases share the same volume and temperature, the individual pressure of each gas is determined solely by its quantity, specifically the number of moles present.
Calculating Total Pressure: The Mathematics
Dalton’s Law is expressed mathematically as the summation: \(P_{\text{Total}} = P_1 + P_2 + P_3 + \dots\). Here, \(P_{\text{Total}}\) is the total pressure of the gas mixture, and \(P_1\), \(P_2\), and so on, are the partial pressures of each individual gas component.
For example, if Gas A exerts 1 atmosphere (atm) and Gas B exerts 0.5 atm, the total pressure (\(P_{\text{Total}}\)) is 1.5 atm. This formula applies regardless of how many different non-reacting gases are mixed together.
The partial pressure of a specific gas can also be determined using the mole fraction (\(X\)). The mole fraction is the ratio of the moles of that gas (\(n_i\)) to the total moles of all gases (\(n_{\text{Total}}\)) in the mixture. This fractional amount directly corresponds to the fraction of the total pressure it contributes.
The relationship is given by the equation: \(P_i = X_i \cdot P_{\text{Total}}\). If a gas makes up 25% of the total moles in a mixture (\(X_i = 0.25\)), it will contribute 25% of the total pressure.
Real-World Scenarios and Applications
The principles of partial pressure are fundamental in high-risk and high-precision fields. A primary application is in deep-sea scuba diving, where the partial pressure of nitrogen in the breathing gas is a significant concern. As a diver descends, the total ambient pressure increases, raising the partial pressure of all gases in the tank, including nitrogen.
Elevated nitrogen partial pressure can lead to nitrogen narcosis, which impairs judgment. If pressure is reduced too quickly during ascent, dissolved nitrogen can form bubbles in the bloodstream, causing decompression sickness, commonly known as “the bends.” Dive tables and specialized gas mixtures like Nitrox use Dalton’s Law to manage these partial pressures safely.
In medical settings, such as anesthesia and respiratory therapy, Dalton’s Law is used to precisely control gas mixtures administered to patients. Anesthesiologists calculate the exact partial pressures of gases like oxygen and anesthetic vapors to ensure the correct dosage. Maintaining a specific oxygen partial pressure is necessary for effective blood oxygenation while avoiding toxicity.
Another application occurs in chemistry laboratories when collecting gas samples over water. Gas produced during a reaction is captured in a container inverted over water, resulting in a mixture with water vapor. To find the true pressure of the collected gas, the partial pressure of the water vapor, which depends on the water’s temperature, must be subtracted from the total measured pressure.