Pressure molecular view

Figure 12-10 is a molecular view showing that the equilibrium concentration of a dissolved gas varies with the partial pressure of that gas. An increase in the partial pressure of gas results in an increase in the rate at which gas molecules enter the solution. This increases the concentration of gas in solution. The increased concentration in solution, in turn, results in an increase in the rate at which gas molecules escape from the solution. Equilibrium is reestablished when the solute concentration is high enough that the rate of escape equals the rate of capture. 

Molecular view of a gasnsolution equilibrium, (a) At equilibrium, the rate of escape of gas molecules from the solution equals the rate of capture of gas molecules by the solution, (b) An increase in gas pressure causes more gas molecules to dissolve, throwing the system out of equilibrium, (c) The concentration of solute increases until the rates of escape and capture once again balance. 

Figure 12-11 is a molecular view of how a solute changes this liquid-vapor equilibrium of the solvent. The presence of a solute means that there are fewer solvent molecules at the surface of the solution. As a result, the rate of solvent evaporation from a solution is slower than the rate of evaporation of pure solvent. At equilibrium, the rate of condensation must be correspondingly slower than the rate of condensation for the pure solvent at equilibrium with its vapor. In other words, the vapor pressure drops when a solute is added to a liquid. A solute decreases the concentration of solvent molecules in the gas phase by reducing the rates of both evaporation and condensation. 

This molecular view of Figure 12-11 suggests that the extent of vapor pressure lowering will depend on the fraction of solvent molecules that has been replaced. In other words, the vapor pressure should be proportional to the mole fraction of the solvent. The molecular view also suggests that this effect does not depend on the nature of the solute, but only on its mole fraction. Experiments show that this is often the case, particularly for dilute solutions. A simple equation, Raoult s law, expresses this proportionality between vapor pressure and mole fraction V V /Jpuj-g solvent Raoulfs law states that the vapor pressure of a solution is the... 

The figure represents a molecular view of a gas-phase reaction that has reached equilibrium. Assuming that each molecule in the molecular view represents a partial pressure of 1.0 bar, determine for this... 

The molecular view represents a set of initial conditions for the reaction described in Example. Each molecule represents a partial pressure of 1.0 bar. Determine the equilibrium conditions and redraw the picture to illustrate those conditions. 

The problem asks for the equilibrium pressures and a molecular view illustrating the equilibrium conditions. 

FIGURE 11.8 A molecular view of Henry s law. (a) At a given pressure, an equilibrium exists in which equal numbers of gas particles enter and leave the solution, (b) When pressure is increased by pushing on the piston, more gas particles are temporarily forced into solution than are able to leave, so solubility increases until a new equilibrium is reached (c). 

In the kinetic-molecular theory pressure is viewed as the result of collisions of gas molecules with the walls of the container. As each molecule strikes a wall, it exerts a small impulse. The pressure is the total force thus exerted on the walls divided by the area of the walls. The total force on the walls (and thus the pressure) is proportional to two factors (1) the... 

The presence of a solute causes vapor-pressure lowering of a solvent. If the solute is nonvolatile (nonevaporating), the solution has a lower vapor pressure than the pure solvent does. (Review vapor pressure in Chapter 7.) From a molecular view, the solute particles at the surface of the liquid inhibit the movement of solvent molecules from going into the vapor phase, but do not inhibit solvent molecules in the vapor phase from returning to the liquid phase, so the rate of evaporation is lower than the rate of condensation until there are fewer solvent molecules in the vapor phase. For solving problems, the vapor pressure of any component (call it A) in the solution. Pa, is related to the vapor pressure of the pure substance, P, by Raoult s law ... 

Under appropriate conditions of pressure and temperature, most substances can exist as a solid, a liquid, or a gas. In Chapter 1 we described these physical states in terms of how each fi 11s a container and began to develop a molecular view that explains this macroscopic behavior a solid has a fixed shape regardless of the container shape because its particles are held rigidly in place a liquid conforms to the container shape but has a definite volume and a surface because its particles are close together but free to move around each other and a gas fills the container because its particles are far apart and moving randomly. Several other aspects of their behavior distinguish gases from liquids and solids ... 

With T-i lower than Tz, the most probable molecular speed u-, is less than U2. (Note the similarity to Figure 5.12) The fraction of molecules with enough energy to escape the liquid (shaded area) is greater at the higher temperature. The molecular views show that at the higher T, equilibrium is reached with more gas molecules in the same volume and thus at a higher vapor pressure. 

Figure 5.17 Molecular view of an ideal gas occupying a cubic box of side length L. The pressure on the shaded wall is calculated explicitly in this section.

FIGURE 11.13 Volume versus pressure a molecular view As... 

A FIGURE 11.17 Volume versus temperature a molecular view If a balloon is moved from an ice-water bath into a boiling-water bath, the gas molecules inside it move faster due to the increased temperature. If the external pressure remains constant, the molecules will expand the balloon and collectively occupy a larger volume. 

That is, for a given amount of gas at a fixed temperature, Ihe pressure times the volume equals a constant. Table 5.3 gives some pressure and volume data for l.(XX) g O2 at 0°C. Figure 5.6 presents a molecular view of the pressure-volume relationship... 

Figure 13.5 A molecular view of Hemy s law. When the partial pressure of the gas over the solution increases from (a) to (b). the concentration of the dissolved gas also increases according to Equation 13.3.

Many properties and qualities of substances, such as the temperature dependence of the pressure of gases, were well understood before the development of quantum theory. With the detailed molecular view obtained with quantum mechanical analysis, an even more fundamental basis for macroscopic chemical phenomena is at hand. 

In the second picture, an interfacial layer or region persists over several molecular diameters due to a more slowly decaying interaction potential with the solid (note Section X-7C). This situation would then be more like the physical adsorption of vapors (see Chapter XVII), which become multilayer near the saturation vapor pressure (e.g.. Fig. X-15). Adsorption from solution, from this point of view, corresponds to a partition between bulk and interfacial phases here the Polanyi potential concept may be used (see Sections X-7C, XI-1 A, and XVII-7). 

As a consequence of these simple deductions, Graham s experiments c effusion through an orifice came to be regarded as one of the earliest direct experimental checks on the kinetic theory of gases. However, a closer examination of his experimental conditions reveals that this view is mistaken. As mentioned earlier, his orifice diameters ranged upwards from 1/500 in., while the upstream pressure was never very much less thai atmospheric. Under these circumstances the molecular mean free path len ... 

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