Gases molar concentration

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

Traditional chemical kinetics uses notation that is most satisfactory in two cases all components are gases with or without an inert buffer gas, or all components are solutes in a Hquid solvent. In these cases, molar concentrations represented by brackets, are defined, which are either constant throughout the system or at least locally meaningful. The reaction quotient Z is defined as... 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

Of course, you should be familiar with this equation (the Ideal Gas Law), where n is the molar concentration of solute, R is the universal gas law constant, and T is absolute temperature in °K. The permeate flow can be calculated from ... 

For example, in the case of dilute solutions, the van t Hoff s equation may be used to piedict the osmotic pressure (jr = CRT) where n is the osmotic pressure of the solution, C is the molar concentration of the solute, ft is the universal gas constant and T is the absolute temperature, Fm dissociating solutes, the concentration is that of the total ions. For example, NaCI dissociates in water into two ions Na" " and Cl . Therefore, the total molar concentration of ions is hvice the molar concentration of NaCI. A useful rule of thumb for predicting osmotic pressure of aqueous solutions is 0,01 psi/ppm of solute (Weber, 1972). 

FIGURE 5.10 Effects of co-expressed G-protein (G ) on neuropeptide NPY4 receptor responses (NPY-4). (a) Dose-response curves for NPY-4. Ordinates Xenopus laevis melanophore responses (increases light transmission). Ordinates logarithms of molar concentrations of neuropeptide Y peptide agonist PYY. Curves obtained after no co-transfection (labeled 0 jig) and co-transfection with cDNA for Gai6. Numbers next to the curves indicate jig of cDNA of Ga]g used for co-transfection, (b) Maximal response to neuropeptide Y (filled circles) and constitutive activity (open circles) as a function of pg cDNA of co-transfected G g. 

For an ideal gas, the total molar concentration Cj is constant at a given total pressure P and temperature T. This approximation holds quite well for real gases and vapours, except at high pressures. For a liquid however, CT may show considerable variations as the concentrations of the components change and, in practice, the total mass concentration (density p of the mixture) is much more nearly constant. Thus for a mixture of ethanol and water for example, the mass density will range from about 790 to 1000 kg/m3 whereas the molar density will range from about 17 to 56 kmol/m3. For this reason the diffusion equations are frequently written in the form of a mass flux JA (mass/area x time) and the concentration gradients in terms of mass concentrations, such as cA. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

As we saw in Section G, the molar concentration of any substance is the amount of molecules (n, in moles) divided by the volume that they occupy (V). It follows from the ideal gas law that, for a gas behaving ideally (so we can write n = PV/RT),... 

This expression shows that, for a given pressure and temperature, the molar concentration should be the same for every gas. That is, two gas samples of equal volume at the same temperature and pressure should contain the same amount of... 

The molar concentrations and densities of gases increase as they are compressed but decrease as they are heated. The density of a gas depends on its molar mass. 

Almost all aquatic organisms rely on the presence of dissolved oxygen for respiration. Although oxygen is nonpolar, it is very slightly soluble in water and the extent to which it dissolves depends on its pressure. We have already seen (in Section 4.2) that the pressure of a gas arises from the impacts of its molecules. When a gas is introduced into the same container as a liquid, the gas molecules can burrow into the liquid like meteorites plunging into the ocean. Because the number of impacts increases as the pressure of a gas increases, we should expect the solubility of the gas—its molar concentration when the dissolved gas is in dynamic equilibrium with the free gas—to increase as its pressure increases. If the gas above the liquid is a mixture (like air), then the solubility of each component depends on that component s partial pressure (Fig. 8.21). 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

The equilibrium constant in Eq. 2 is defined in terms of activities, and the activities are interpreted in terms of the partial pressures or concentrations. Gases always appear in K as the numerical values of their partial pressures and solutes always appear as the numerical values of their molarities. Often, however, we want to discuss gas-phase equilibria in terms of molar concentrations (the amount of gas molecules in moles divided by the volume of the container, [I] = j/V), not partial pressures. To do so, we introduce the equilibrium constant Kt., which for reaction E is defined as... 

For thermodynamic calculations, gas-phase equilibria are expressed in terms of K but, for practical calculations, they may be expressed in terms of molar concentrations by using Eq. 12. 

Suppose that we were to increase the total pressure inside a reaction vessel by pumping in argon or some other inert gas at constant volume. The reacting gases continue to occupy the same volume, and so their individual molar concentrations and partial pressures remain unchanged despite the presence of an inert gas. In this case, therefore, provided that the gases can be regarded as ideal, the equilibrium composition is unaffected despite the fact that the total pressure has increased. 

If the reaction involves gas-phase species and the rate law is expressed in terms of molar concentrations, then instead of K use Kc. 

Hydrogen bums in an atmosphere of bromine to give hydrogen bromide. If 135 mL of H, gas at 273 K and LOO atm combines with a stoichiometric amount of bromine and the resulting hydrogen bromide dissolves to form 225 mL of an aqueous solution, what is the molar concentration of the resulting hydrobromic acid solution ... 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

Let us say that this new surface equilibrium temperature of the water is 15.5 °C then the vapor pressure is 0.0174 atm. At the surface of the water, not only does water vapor exist, but so must the original gas mixture components of air, O2 and N2. By Dalton s law the molar concentration of the water vapor is... 

CTOT total molar concentration of gas phase (niol/mgfls3)... 

This reaction quotient is a fraction. The numerator is the product of the chemical species on the right hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. The denominator is the product of the chemical species on the left hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. It is called Qc, in this case, since molar concentrations are being used. If this was a gas phase reaction, gas pressures could be used and it would become a Qp. 

For fixed time assays this most frequently involves the use of standards and a calibration graph. Some methods, e.g. the use of the molar absorbance coefficient in spectrophotometry, do not requite standards and giiNometric methods permit the calculation of molar concentration from the volume of gas (1 gram mole of gas occupies 22.4 litres at standard temperature and pressure, STP). 

CAe Molar concentration of A in liquid phase in equilibrium with partial pressure Pag in gas phase kmol/m3 NL-3... 

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