Graham's Law Research Articles

Diffusion Rates on the Overhead Projector: Amines Compared to HCl

Diffusion rates of selected amines are compared to that of HCl using a method very similar to those described for NH3 versus HCl diffusion. Well-defined white amine hydrochloride rings form quickly and Graham's Law can be tested for different molar masses.

A liquid-phase diffusion experiment

Substituting liquid-phase diffusion of various aqueous ions for classic gas-phase diffusion of HCL and NH4Cl to illustrate Graham's Law of Diffusion; sample data and analysis included.

Misuse of Graham's laws

Misuse of Graham's laws

Flow of Air, Nitrogen, and Hydrogen through Porous Glass Tubes

Abstract A simple apparatus for obtaining diffusion data for porous tubes is described. It was used for determining the permeation rates of air, nitrogen, and hydrogen through porous 96% SiO2 glass tubes. To increase flow, these tubes were subjected to multiple etch/wash treatments using aqueous NH4F solutions at room temperature followed by successive hot washes in dilute mineral acid and distilled water. Further increases in permeation rates were achieved by subjecting the base glass used in the preparation of the porous glass to long heat treatments at its phase-separation liquidus prior to leaching and etching. Diffusion data show that the permeability of porous glass is not degraded on heating at temperatures up to 800°C, and that the separation ratios of the experimental glasses are in good agreement with values expected from Graham's law of diffusion. The role of heat treatment of the base glass, etch/wash treatments of the porous glass, and moisture in the gas stream are discussed.

Measuring the ratio of aqueous diffusion coefficients between 6Li +Cl − and 7Li +Cr − by osmometry

Osmotic equilibrium is a singular occurrence in the evolution of an osmotic cell because at this event the net solution flux is zero such that −J w · V ̄ w = J s · V ̄ s . At this juncture, the diffusion coefficient of the solute through the membrane (ω) equals the solute flux ( J s ) divided by the osmotic pressure (ΔΠ). Because the solute permeability coefficient (ω) is related to the Fickian diffusion coefficient ( D) through the gas constant, temperature, and the membrane's thickness and tortuosity, the ratio of ω values for individual isotopic species equals the ratio of D values for the same isotopic components. A 0.9450 molal LiCl solution was placed within sealed dialysis tubing and osmoted against a kilogram of deionized water at 22°C. Osmotic equilibrium occurred at 164 ± 10 min. The ratio of ω6Li +Cl − ω7Li +Cl − was measured to be 1.011 ± 0.003—a value close to the square root of the mass ratio between 7LiCl and 6LiCl (= 1.012) as calculated by Graham's Law. The measured diffusion coefficient ratio was used to predict the degree of hyperfiltration-induced fractionation of Li isotopes as a function of membrane ideality. When a membrane's σ exceeds 0.95 (as is likely for low-porosity shales) the 6Li 7Li ratio on the high-pressure side of the membrane can theoretically vary by more than 0.0017.

Overhead projection of Graham's law of gaseous diffusion

Demonstration of gaseous diffusion through the combination of NH3 and HCl to produce NH4Cl.

Graham's law: Defining gas velocities

Graham's law: Defining gas velocities

The BedBugs game: A molecular motion simulator

Using the electronic game BedBugs to simulate molecular motion and illustrate diffusion, effusion, and Graham's law.

A simple apparatus to demonstrate differing gas diffusion rates (Graham's law)

The apparatus described in this note dramatically demonstrates relative diffusion rate effects for common gases like methane and carbon dioxide.

Experimental confirmation of Graham's law of diffusion up to pore diameters of 2 μm

Gas counterdiffusion of helium and air through membranes at uniform pressure is investigated theoretically and experimentally. By varying the pore diameter of a membrane from 0.015 μm to 2.0 μm, experiments with the two gases are carried out in the Knudsen region and in the transition region at atmospheric pressure.The selectivity of the membranes can be concluded from the experimental results. It is shown that the ratio of the molar fluxes is given by Graham's law, i.e. in isobaric counterdiffusion the molar flux is inversely proportional to the square root of the molar weight.For large pore diameters with respect to the mean free path of the gas molecules, the selectivity is extremely sensitive to pressure fluctuations as a non-selective laminar flow occurs. Therefore, in industrial applications, membranes should be used where the condition for Knudsen diffusion prevails.

A novel cell for gas-counterdiffusion measurements in porous pellets

A new type of isobaric diffusion cell for measuring the countercurrent gas diffusion in porous catalyst pellets at atmospheric pressure is proposed. To determine the diffusion fluxes, the rate of change of gas volume in one part of the cell is measured, which follows from Graham's law; this change corresponds to the rise of a soap bubble film in a calibrated burette. To obtain the information needed for evaluating the parameters of equations describing diffusion transport in a porous medium the use of several pairs of gases is proposed. The method of evaluating transport parameters from diffusion measurements of this type is demonstrated for the mean transport-pore model.

Value and limits of Graham's law for prediction of diffusivities of gases in gas mixtures

The validity of Graham's law, i.e. the inversely proportional relationship between diffusivity (diffusiom coefficient) and the square root of the molecular mass, is tested for test gases and gas mixtures of physiological interest based on recent measurements of diffusivities of gases in gas phase. With gases of medium molecular mass (10 to 30 g/mol) predictions on the basis of Graham's law are reasonably accurate, deviations from experimental values not exceeding 20%. With gases of high and low molecular masses, however, larger discrepancies are encountered. The prediction of diffusion coefficients on the basis of the Chapman-Enskog theory is in most cases more accurate than that based on Graham's law.

Diffusion of gaseous fluoromethanes in air

A simple uniform-pressure diffusion apparatus has been used to measure the diffusivities of the gaseous fluorocarbons CF 4 and CF 2Cl 2 in air at atmospheric pressure and room temperature (293 K). The diffusion coefficients are found to be D(CF 4—air) = 0.121 cm 2s −1 and D(CF 2Cl 2—air) = 0.098 cm 2s −1. The observed diffusion flux ratios are in agreement with Graham's diffusion law.

Diffusivity of various inert gases in rat skeletal muscle

Krogh's diffusion constant (K) was determined for various inert gases in isolated rat abdominal muscle at 37 degrees C by measuring the amount of gas diffusing per unit time and partial pressure difference through a portion of the muscle of known surface area and thickness. The following mean values for K, in 10(-9) mmol-min-1-cm-1-torr-1, were obtained: C2H2, 42.2; N2O, 20.0; CHClF2, 18.8; H2, 1.67; He, 1.42; CH4, 1.27; SF6, 0.081. From Krogh's diffusion constant, the diffusion coefficient (D) was calculated using the solubility coefficient determined previously in the same preparation. The D values thus obtained were found to be about half the D values in water at 37 degrees C. Model calculations show that for gases with high lipid/water partition coefficient, D in tissues containing lipid is underestimated by this method. Graham's law (inverse proportionality between D and square root of molecular mass) was found to represent a useful approximation for these gases. A better correlation, however, was obtained between D and the molecular diameter.

Are we teaching the most useful ideas about transport?

Argues that Einstein's laws of diffusion are more important than Graham's law of diffusion.

Stochastic relations for diffusion at strictly uniform pressure in imperfect gases

In the light of recent work on gaseous diffusion, emphasizing the importance of the distinction between (a) diffusion at strictly uniform pressure (the situation with which Graham's law of diffusion is concerned), and (b) interdiffusion in an enclosed space, attention is paid to the systematic elementary stochastic treatment of both, for both ideal and non-ideal gaseous mixtures. The present investigation may be considered an extension and clarification of Yang's stochastic treatment of diffusion in fluids.

Diffusion at strictly uniform pressure in a mixture of a dissociating gas and an inert gas

In the light of recent revived interest in Graham's law of diffusion, attention is given to the diffusive fluxes in a mixture of a dissociating and an inert gas, in conditions in which the pressure is strictly uniform. Explicit expressions are given for the continuum limit, in the case in which there is local chemical equilibrium. The quotient of the fluxes of the dissociating gas and the inert gas (expressed in terms of masses, rather than in terms of numbers of molecules) can be interpreted as the square root of the ratio of an effective molecular weight of the dissociating gas to the molecular weight of the inert gas. This effective molecular weight depends not only on the extent of dissociation but also on diffusion coefficients. For an isomerizing gas, however, the effective molecular weight is simply equal to the true molecular weight.

Graham's laws

Abstract Many textbooks give an inadequate, and even inaccurate, presentation of the laws established by Graham on diffusion and related topics. These laws are fundamental to the understanding of the motion of gases in porous solids, and, stemming to a considerable extent from applied research on reactions of gases in porous catalysts, and on gas-cooled nuclear reactors, a better appreciation of the significance of the laws has been attained in recent years. A survey is given of Graham's actual findings, and their relation to other investigations, in the light of recent research.

Carbon Dioxide Exchanges in Leaves. I. Discrimination Between 14CO2 and 12CO2 in Photosynthesis

In order to measure CO(2) exchange reactions by leaves using isotopes of CO(2), it is necessary to know precisely the discrimination against (14)CO(2) by leaves. Earlier determinations of discrimination are at variance, and may be inaccurate because of assumptions made about the rate of photorespiration. Maize leaves evolve little or no CO(2) in light, and so provide suitable material for this measurement. Discrimination against (14)CO(2) in photosynthesis by maize leaves is almost precisely the same as in CO(2) absorption by NaOH solution, amounting to 2.1 and 2.0% respectively. The agreement between these values and their close approximation to the relative rates of diffusion of (12)CO(2) and (14)CO(2), calculated from Graham's law, shows that diffusion into the leaf is primarily responsible for discrimination against (14)CO(2) in photosynthesis.

Graham's laws: Simple demonstrations of gases in motion: Part II, Experiments

Graham's laws: Simple demonstrations of gases in motion: Part II, Experiments