## Gas Diffusion and Effusion

Due to their constant, random motion, gas molecules diffuse into areas of lower concentration, and effuse through tiny openings.

### Learning Objectives

Explain the concepts of diffusion and effusion.

### Key Takeaways

#### Key Points

• Gaseous particles are in constant random motion.
• Gaseous particles tend to undergo diffusion because they have kinetic energy.
• Diffusion is faster at higher temperatures because the gas molecules have greater kinetic energy.
• Effusion refers to the movement of gas particles through a small hole.
• Graham’s Law states that the effusion rate of a gas is inversely proportional to the square root of the mass of its particles.

#### Key Terms

• diffusion: movement of particles from an area of high concentration to one of low concentration
• mean free path: the average distance traveled by a particle between collisions with other particles
• Effusion: movement of gas molecules through a tiny hole

### Diffusion

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.

Diffusion refers to the process of particles moving from an area of high concentration to one of low concentration. The rate of this movement is a function of temperature, viscosity of the medium, and the size (mass) of the particles. Diffusion results in the gradual mixing of materials, and eventually, it forms a homogeneous mixture.

Diffusion: Particles in a liquid-filled beaker are initially concentrated in one area, but diffuse from their area of high concentration to the areas of low concentration until they are distributed evenly throughout the liquid.

### Effusion

Not only do gaseous particles move with high kinetic energy, but their small size enables them to move through small openings as well; this process is known as effusion. For effusion to occur, the hole’s diameter must be smaller than the molecules’ mean free path (the average distance that a gas particle travels between successive collisions with other gas particles). The opening of the hole must be smaller than the mean free path because otherwise, the gas could move back and forth through the hole.

Effusion is explained by the continuous random motion of particles; over time, this random motion guarantees that some particles will eventually pass through the hole.

Interactive: Diffusion & Temperature: Explore the role of temperature on the rate of diffusion. Set the temperature, then remove the barrier, and measure the amount of time it takes the blue molecules to reach the gas sensor. When the gas sensor has detected three blue molecules, it will stop the experiment. Compare the diffusion rates at low, medium and high temperatures. Trace an individual molecule to see the path it takes.

Interactive: Diffusion and Molecular Mass: Explore the role of a molecule’s mass with respect to its diffusion rate.

### Graham’s Law

Scottish chemist Thomas Graham experimentally determined that the ratio of the rates of effusion for two gases is equal to the square root of the inverse ratio of the gases’ molar masses. This is written as follows:

$\frac{\text{rate of effusion gas 1}}{\text{rate of effusion gas 2}}=\sqrt{\frac{M_2}{M_1}}$

where M represents the molar mass of the molecules of each of the two gases.

The gases’ effusion rate is directly proportional to the average velocity at which they move; a gas is more likely to pass through an orifice if its particles are moving at faster speeds.

### Example

What is the ratio of the rate of effusion of ammonia, NH3, to that of hydrogen chloride, HCl?

$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}}=\sqrt{\frac{36.46\text{ g/mol}}{17.03\text{ g/mol}}}=1.46$

The NH3 molecules effuse at a rate 1.46 times faster than HCl molecules.

### Derivation of Graham’s Law

Graham’s Law can be understood as a consequence of the average molecular kinetic energy of two different gas molecules (marked 1 and 2) being equal at the same temperature. (Recall that a result of the Kinetic Theory of Gases is that the temperature, in degrees Kelvin, is directly proportional to the average kinetic energy of the molecules.) Therefore, equating the kinetic energy of molecules 1 and 2, we obtain:

$\frac{1}{2}m_1v_1^2 = \frac{1}{2}m_2v_2^2$

$m_1v_1^2 = m_2v_2^2$

$\frac{v_1^2}{v_2^2}=\frac{m_2}{m_1}$

$\frac{v_1}{v_2}=\frac{\sqrt{m_2}}{\sqrt{m_1}}$

The rate of effusion is determined by the number of molecules that diffuse through the hole in a unit of time, and therefore by the average molecular velocity of the gas molecules.

## Osmosis

Osmosis is the movement of water across a membrane from an area of low solute concentration to an area of high solute concentration.

### Learning Objectives

Describe the process of osmosis and explain how concentration gradient affects osmosis

### Key Takeaways

#### Key Points

• Osmosis occurs according to the concentration gradient of water across the membrane, which is inversely proportional to the concentration of solutes.
• Osmosis occurs until the concentration gradient of water goes to zero or until the hydrostatic pressure of the water balances the osmotic pressure.
• Osmosis occurs when there is a concentration gradient of a solute within a solution, but the membrane does not allow diffusion of the solute.

#### Key Terms

• solute: Any substance that is dissolved in a liquid solvent to create a solution
• osmosis: The net movement of solvent molecules from a region of high solvent potential to a region of lower solvent potential through a partially permeable membrane
• semipermeable membrane: A type of biological membrane that will allow certain molecules or ions to pass through it by diffusion and occasionally by specialized facilitated diffusion

### Osmosis and Semipermeable Membranes

Osmosis is the movement of water through a semipermeable membrane according to the concentration gradient of water across the membrane, which is inversely proportional to the concentration of solutes. Semipermeable membranes, also termed selectively permeable membranes or partially permeable membranes, allow certain molecules or ions to pass through by diffusion.

While diffusion transports materials across membranes and within cells, osmosis transports only water across a membrane. The semipermeable membrane limits the diffusion of solutes in the water. Not surprisingly, the aquaporin proteins that facilitate water movement play a large role in osmosis, most prominently in red blood cells and the membranes of kidney tubules.

### Mechanism of Osmosis

Osmosis is a special case of diffusion. Water, like other substances, moves from an area of high concentration to one of low concentration. An obvious question is what makes water move at all? Imagine a beaker with a semipermeable membrane separating the two sides or halves. On both sides of the membrane the water level is the same, but there are different concentrations of a dissolved substance, or solute, that cannot cross the membrane (otherwise the concentrations on each side would be balanced by the solute crossing the membrane). If the volume of the solution on both sides of the membrane is the same but the concentrations of solute are different, then there are different amounts of water, the solvent, on either side of the membrane. If there is more solute in one area, then there is less water; if there is less solute in one area, then there must be more water.

To illustrate this, imagine two full glasses of water. One has a single teaspoon of sugar in it, whereas the second one contains one-quarter cup of sugar. If the total volume of the solutions in both cups is the same, which cup contains more water? Because the large amount of sugar in the second cup takes up much more space than the teaspoon of sugar in the first cup, the first cup has more water in it.

Osmosis: In osmosis, water always moves from an area of higher water concentration to one of lower concentration. In the diagram shown, the solute cannot pass through the selectively permeable membrane, but the water can.

Returning to the beaker example, recall that it has a mixture of solutes on either side of the membrane. A principle of diffusion is that the molecules move around and will spread evenly throughout the medium if they can. However, only the material capable of passing through the membrane will diffuse through it. In this example, the solute cannot diffuse through the membrane, but the water can. Water has a concentration gradient in this system. Thus, water will diffuse down its concentration gradient, crossing the membrane to the side where it is less concentrated. This diffusion of water through the membrane—osmosis—will continue until the concentration gradient of water goes to zero or until the hydrostatic pressure of the water balances the osmotic pressure. In the beaker example, this means that the level of fluid in the side with a higher solute concentration will go up.