Molar concentration of a gas

The molar concentration of a gas and a related quantity, the density of a gas, are both of great interest to meteorologists as well as to engineers. As we saw in Section G, the molar concentration is the number of moles of molecules divided by the volume of the sample (n/V). It follows from the ideal gas law that, for a gas behaving ideally,... 

Because we now have two alternative definitions for equilibrium constants, it is appropriate to ask whether they will lead to the same values. 1b answer that question, we need to relate the molar concentration of a gas to its partial pressure. That connection can be made through the ideal gas law and more specifically by Equation 5.5 (page 170), which defines the partial pressure of a gas / ... 

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). 

The mathematical machinery of thermod3mamics allows this qualitative statement to be expressed quantitatively. Experiments and theory show that the molar entropy of a gas or solute varies logarithmically with concentration... 

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

Here [A] is the gas-phase molar concentration of A above the surface, for example, in mol/cm3. Assuming that the total site density T is fixed and that the surface population consists of either adsorbed species A(s) or open sites O(s),... 

Dj is the mass diffusion coefficient, and cgas is the total molar concentration of the gas mixture. Although Equations (3.9a) and (3.9b) can be used for a free-path gas (e.g. gas channel), when a gas is moving within a porous media (i.e. electrode), Equation (3.9) may not be the most appropriate. Different constitutive laws can be employed for describing the diffusive flux within a porous medium. The choice of the most appropriate law depends on the operating conditions and the porous media properties, as further explained in Section 3.3.2. 

C Using solubility data of a gas in a solid, explain how you would determine the molar concentration of the gas in the solid at the solid-gas interface at a specified temperature. 14-32C Using Henry s constant data for a gas dissolved in a liquid, explain how you would determine the mole fraction of the gas dissolved in the liquid al the interface at a specified tempemture. 14-33C What is permeability How is the permeability of a gas in a solid related to the solubility of the gas in that solid 14-34 Determine the mole fraction of carbon dioxide (CO2) dissolved in water at the surface of water at 300 K. The mole fraction of CO in air is 0.005, and the local atmosphere pressure is 100 kPa. 

There are ways other than density to include volume in stoichiometry problems. For example, if a substance in the problem is a gas at standard temperature and pressure (STP), use the molar volume of a gas to change directly between volume of the gas and moles. The molar volume of a gas is 22.41 L/mol for any gas at STP. Also, if a substance in the problem is in aqueous solution, then use the concentration of the solution to convert the volume of the solution to the moles of the substance dissolved. This procedure is especially useful when you perform calculations involving the reaction between an acid and a base. Of course, even in these problems, the basic process remains the same change to moles, use the mole ratio, and change to the desired units. 

The volume for volume system of specifying concentrations of a gas in a gas is dimensionless (without units) (i.e., it represents a pure ratio of volumes in the same volume units) which, thus, allows the units to divide out. To a chemist, this system has the further advantage that comparisons made on a volume for volume basis are also on a molecular, or molar basis (i.e., a mole of any gas at normal temperature and pressure-NTP or STP 0°C and 1 atm) occupies 22.41 L. This volume for volume comparison is true for most gases and vapors when existing in the form of mixtures at or near ambient conditions of pressure and temperature, and only deviates significantly from this molar equivalency when the conditions (pressure and/or temperature) become extreme. When using this system it must be remembered that volume for volume data are corrected to 25°C and 1 atm, when a molar volume corresponds to 24.5 (24.46) L (298 K/273 K x 22.41 L). 

The molar concentration of this gas is just (nilV). Switching fi-om i to A to match our generalized reaction, we can write... 

P is in direct proportion to n/V, which is the molar concentration of the gas. Therefore, a lower concentration of a gaseous reactant within the catalyst layer will result in a lower partial pressure and then a lower electrode potential. 

You can think of the activity as the molar concentration of a solution component or the partial pressure of a gas with the unitsomitted. 

We can now proceed to a direct calculation. The difference in pressure (dP) between the upper and lower part of element dz corresponds to the weight of this element, with M as the molar mass and C the molar concentration of the gas ... 

Since a perfect gas behavior was assumed in the derivation of Eq, (6.76), caution is advised in the use of this equation when the pressure of the gas mixture deviates appreciably from this assumption. For example, experimental measurements have shown that the actual water vapor content in air will be over four times that predicted by ideal gas behavior at a temperature of — 227K and a pressure of 20.2 MPa. Familiarity with these deviations is necessary if problems are to be avoided with this method of impurity removal. Data of this type are available as enhancement factors, defined as the ratio of the actual molar concentration to the ideal molar concentration of a specific impurity in a given gas. 

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. 

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. 

In distillation, equimolecular counterdiffusion takes place if the molar latent heats of the components are equal and the molar rate of flow of the two phases then remains approximately constant throughout the whole height of the column. In gas absorption, however, the mass transfer rate is increased as a result of bulk flow and, at high concentrations of soluble gas, the molar rate of flow at the top of the column will be less than that at the bottom, At low concentrations, however, bulk flow will contribute very little to mass transfer and, in addition, flowrates will be approximately constant over the whole column. 

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. 

Carbon dioxide is absorbed in alkaline water from a mixture consisting of 30% CO2 and 70% Nj and the mass transfer rate is 0.1 kmobs. The concentration of CO2 in the gas in contact with the water is effectively zero. The gas is then mixed with an equal molar quantity of a second gas stream of molar composition 20% CO2, 50%, N2 and 30% H2. What will be the new mass transfer rate, if the surface area, temperature and... 

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