Total gas pressure

The state of equilibrium differs from the equilibrium between water and pure water vapor in that, in a gas phase, there is also inert gas (dry air) present. This means that the water pressure is equal to the total gas pressure, p -- p, + ph, not to the water vapor pressure p, . 

By replacing the mole fraction of water with the ratio of water vapor pressure (Pw) divided by the total gas pressure (PT), one can solve for the diffusive flux of water vapor. Also, by multiplying Nw by the molecular weight of water, the mass flux of water vapor is arrived at ... 

The most important gas phase analytical techniques are mass spectrometry and gas phase chromatography. If the total gas pressure is <10-4-10-8 Torr, a mass spectrometer such an omegatron or a quadrupole instrument may be inserted into the reactant volume. However, in most cases, the pressure is in excess of this, and gas must be delivered to a mass spectrometer via a leak, such as a Metrosil pellet or a capillary constriction, situated as closely as possible to the reaction volume. 

In an early investigation (28, 59, 60), critical combinations of several reaction parameters were discovered to produce unusually high yields of the linear isomer. The parameters included low partial pressure of carbon monoxide, high concentration of phosphite or aryl phosphine ligands, and low total gas pressure. The catalyst was a soluble complex of rhodium, formed in situ from rhodium metal in many cases. Isomer ratios of 10 1 to 30 1 were obtained by appropriate selection of these reaction parameters. Losses to alkane were minimal, even with Pm as low as 10 psi. Tables XI-XIV illustrate the effects of these various reaction parameters on the product composition. 

As a consequence, a change in overall volume or total gas pressure will have no effect on the position of equilibrium. In the equilibrium constant expression, the two partial pressures in the numerator will be affected to exactly the same degree as the two partial pressures in the denominator, and Qp will continue to equal Kp. 

Because AVp is a function of the total gas pressure, the gas compositions in Figure 6-5 have little influence on AVp. Based on these results, the effect of cell voltage from a change in pressure can be expressed by the equation... 

External conditions of the membrane-water system are given by temperatures (Tg,TJ, vapor pressures and total gas pressures (PJ, PJ) in the... 

Mechanical equilibrium corresponds to the balance of pressures in the system, involving total gas pressure, Ps liquid pressure in the water phase inside the membrane, P capillary pressure, P and elastic pressure exerted by the polymer matrix, P . 

Under fuel cell operation, a finite proton current density, 0, and the associated electro-osmotic drag effect will further affect the distribution and fluxes of water in the PEM. After relaxation to steady-state operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces. External conditions defined by temperature, vapor pressures, total gas pressures, and proton current density are sufficient to determine the stationary distribution and the flux of water. 

For given external vapor pressure and total gas pressure, the liquid pressure (or swelling pressure) in the membrane is obtained from Equations (6.6) and (6.13) ... 

This implies that vapor equilibration of PEMs corresponds to large negative liquid pressures inside the membrane or that Tj, would increase from zero to the saturation value for P very close to P. Moreover, the effect of the total gas pressure on water uptake should be insignificant at normal values of Ps 1 atm. Heuristic solutions out of this dilemma would be to recalibrate the value of V or to normalize P to a reference value of a... 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

P vapor pressure (PEM modeling atm) p capillary pressure (CCL modeling atm) p8 total gas pressure (CCL modeling atm) p liquid pressure (CCL modeling atm) q coulombic charge (C) q" saturated vapour pressure (CCL atm) q vapor pressure (CCL modeling atm)... 

While most models treat gas-phase flow as purely due to diffusion (i.e., the total gas pressure or concentration remains uniform), some models take into account convection in the gas-... 

L = a dimensionless parameter defined by Equation 10 l — liquid depth P = total gas pressure p = partial pressure p0 = vapor pressure R = gas-law constant T — absolute temperature... 

Figure 14.2 Carbon concentration (determined by AES using the sensitivity coefficients of table 1) in fi-WC, and 6-MoC,. films as a function of the temperature of the substrate the total gas pressure was 1.33 Pa and the applied voltage was 3000 V.

Figure 14.6 Effect of pressure of reacting gas on the concentation of the nonmetal in the films (a) M-C systems, the pressure is the total gas pressure (10% CH4/Ar) (b) M-N systems, the pressure is the total gas pressure (pure N2). , Mo , W.

At 20 °C, for y-ray induced copolymerizations, r, 0.04 for monomer compositions containing 8-39% CO 7). At 120-130 °C, for (C2HsO)2 initiated copolymerizations, tj si 0.15 9). As Eq. (6) indicates, there exists one monomer ratio for which the copolymer composition equals the monomer composition, namely if + [C]/[E]) = 1. Using the above values of r, this azeotropic composition corresponds to 48.5 mol % CO for the y-ray induced copolymerizations at 20 °C (Fig. 1) 7), and si 46 mol % CO for the free radical initiated copolymerizations 9). The value of rj is dependent on the reaction temperature. For example, for the y-ray induced copolymerizations, the value of r2 increases from 0.04 at 20 °C to 0.31 at 157 °C 7). As expected, the value of rt at 135 °C was close to that observed for the free-radical initiated polymerization at that temperature. These results indicate that the copolymerization should be carried out at low temperatures in order to get copolymers with high CO contents. The azeotropic composition is also altered by pressure. For example, for (C2HsO)2 initiated copolymerizations the %CO in the azeotropic composition drops from 46% to 36% when the total gas pressure is lowered from 100 to 13.6 MPa (from 1000 to 136 atm) 9). 

The derivation of Equation (2.60) might be seen as a long-winded way of arriving at a trivial result. However, this derivation explicitly clarifies the assumptions behind this equation. First, a gradient in concentration occurs within the membrane, but there is no gradient in pressure. Second, the absorption of a component into the membrane is proportional to its activity (partial pressure) in the adjacent gas, but is independent of the total gas pressure. This is related to the approximation made in Equation (2.52), in which the Poynting correction was assumed to be 1. 

The total gas pressures on the feed and permeate side are the sum of the partial pressures. For the feed side... 

Fig. 3.12. Comparison of two models for estimating the total gas pressure of mixed CH4-CO2 gas hydrates. Reprinted from Marion et al. (2006) with permission...

A dry gas occupied 127 cm3 at S.T.P If this same mass of gas were collected over water at 23°C (total gas pressure 745 torr), what volume would it occupy Water s vapor pressure at 23°C is 21 torr. 

The vapor pressure of water at 80°C is 355 torr. A 100-mL vessel contained water-saturated oxygen at 80°C, the total gas pressure being 760 torr. The contents of the vessel were pumped into a 50-mL vessel at the same temperature. Assuming no condensation, (a) What were the partial pressures of oxygen and of the water vapor (b) What was the total pressure in the final equilibrium state ... 

---