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Partial Pressure and Graham's Law

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Terms you will need

  • partial pressurePartial pressure is the pressure that a single gas in a mixture would exert if it alone occupied the entire volume of the mixture.

How this topic runs

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Partial pressure and Graham's law are essential concepts in understanding the behavior of gases in mixtures. Partial pressure refers to the pressure that a particular gas in a mixture would exert if it occupied the entire volume alone. This concept is crucial for analyzing gas mixtures and their interactions, especially in chemical reactions and physical processes. Graham's law, on the other hand, describes the relationship between the rate of effusion or diffusion of a gas and its molar mass. It states that the rate of effusion is inversely proportional to the square root of the gas's molar mass. These principles are foundational in thermodynamics and chemistry, providing insights into how gases behave under various conditions and how they contribute to the overall properties of a system. Understanding these concepts allows scientists to predict and control gas behavior in both theoretical and practical applications.

Figures (10)

An illustration of Dalton's law using the gases of air at sea level
Figure 9.9 In 1783, the first (a) hydrogen-filled balloon flight, (b) manned hot air balloon flight, and (c) manned hydrogen-filled balloon flight occurred. When the hydrogen-filled balloon depicted in (a) landed, the frightened villagers of Gonesse reportedly destroyed it with pitchforks and knives. The launch of the latter was reportedly viewed by 400,000 people in Paris.
Figure 9.10 The effect of temperature on gas pressure: When the hot plate is off, the pressure of the gas in the sphere is relatively low. As the gas is heated, the pressure of the gas in the sphere increases.
Figure 9.11 For a constant volume and amount of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures because of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero.
Figure 9.12 The volume and temperature are linearly related for 1 mole of methane gas at a constant pressure of 1 atm. If the temperature is in kelvin, volume and temperature are directly proportional. The line stops at 111 K because methane liquefies at this temperature; when extrapolated, it intersects the graph’s origin, representing a temperature of absolute zero.
Figure 9.13 When a gas occupies a smaller volume, it exerts a higher pressure; when it occupies a larger volume, it exerts a lower pressure (assuming the amount of gas and the temperature do not change). Since P and V are inversely proportional, a graph of 1P1P vs. V is linear.
Figure 9.14 The relationship between pressure and volume is inversely proportional. (a) The graph of P vs. V is a hyperbola, whereas (b) the graph of (1P)(1P) vs. V is linear.
Figure 9.15 Breathing occurs because expanding and contracting lung volume creates small pressure differences between your lungs and your surroundings, causing air to be drawn into and forced out of your lungs.
Figure 9.16 Scuba divers use compressed air to breathe while underwater. (credit: modification of work by Mark Goodchild)
Figure 9.17 Scuba divers, whether at the Great Barrier Reef or in the Caribbean, must be aware of buoyancy, pressure equalization, and the amount of time they spend underwater, to avoid the risks associated with pressurized gases in the body. (credit: Kyle Taylor)

In a gas mixture, each gas contributes its own partial pressure, and the total pressure is the sum of all these individual pressures. This concept helps scientists understand how gases behave together in a shared space, like in the air we breathe or in chemical reactions. Graham's law explains how fast a gas spreads out or escapes through a small opening.

It says that lighter gases (with smaller molar masses) move faster than heavier ones. This law is useful in predicting how gases like helium or carbon dioxide will behave in different situations, such as in a balloon or during a chemical process. To picture partial pressure, imagine a container with two gases.

Each gas pushes against the container walls with its own force, and the total pressure is the sum of both. For Graham's law, imagine two gases racing through a tiny hole—lighter ones win the race. These ideas help scientists control and predict gas behavior in real-world settings.

Key Points

  • Partial pressure is the pressure that a particular gas in a mixture would exert if it occupied the same volume alone at the same temperature.
  • Dalton's law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture.
  • Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
  • Molar mass is the mass of one mole of a substance, expressed in grams per mole.

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