The Effect of a Change in Pressure Volume

Changes in pressure have significant effects only on equilibrium systems with gaseous components. Aside from phase changes, a change in pressure has a negligible effect on liquids and solids because they are nearly incompressible. Pressure changes can occur in three ways  

On the other hand, changing the pressure by changing the volume often causes a large shift in the equilibrium position. Suppose we let the PCI3-CI2-PCI5 system come to equilibrium in a cylinder-piston assembly. Then, we press down on the piston to halve the volume the gas pressure immediately doubles. To reduce this increase in gas pressure, the system responds by reducing the number of gas molecules. And it does so in the only possible way—by shifting the reaction toward the side with fewer moles of gas, in this case, toward the product side  

Notice that a change in volume results in a change in concentration a decrease in container volume raises the concentration, and an increase in volume lowers 

In many cases, however, gas does not change (A gas = 0). For example, 

Therefore, a change in volume has the same effect on the numerator and denominator. Thus, if Augas = 0, there is no effect on the equilibrium position. 

SAMPLE PROBLEM 17.10 Predicting the Effect of a Change in Volume (Pressure) 

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Figure 17.8 The effect of a change in pressure (volume) on a system at equilibrium. The system of...

The effect of a change in pressure is to change both the allowable velocity and actual flowing volume. The net effect of an increase in pressure is an increased capacity expressed in standard cubic feet. Note, however. 

The discussion above has been directed principally to thermally induced spin transitions, but other physical perturbations can either initiate or modify a spin transition. The effect of a change in the external pressure has been widely studied and is treated in detail in Chap. 22. The normal effect of an increase in pressure is to stabilise the low spin state, i.e. to increase the transition temperature. This can be understood in terms of the volume reduction which accompanies the high spin—dow spin change, arising primarily from the shorter metal-donor atom distances in the low spin form. An increase in pressure effectively increases the separation between the zero point energies of the low spin and high spin states by the work term PAV. The application of pressure can in fact induce a transition in a HS system for which a thermal transition does not occur. This applies in complex systems, e.g. in [Fe (phen)2Cl2] [158] and also in the simple binary compounds iron(II) oxide [159] and iron(II) sulfide [160]. Transitions such as those in these simple binary systems can be expected in minerals of iron and other first transition series metals in the deep mantle and core of the earth. 

EFFECTS OF CHANGING THE VOLUME Le Chatelier s principle also predicts the effect of a change in volume on gas-phase equilibrium. Decreasing the volume of a gaseous system increases its total pressure, and the system responds, if possible, to reduce the total pressure. For example, in the equilibrium... 

The value 2370 kJ/kg is not the latent heat of vaporization of water at 25 C (2440 kJ/kg) but includes the effect of a change from a heating value at constant volume to one at constant pressure (—70 kJ/kg) as described in a later section of this chapter. 

Three key relationships exist among the four gas variables—Boyle s, Charles s, and Avogadro s laws. Each of these gas laws expresses the effect of one variable on another, with the remaining two variables held constant. Because gas volume is so easy to measure, the laws are expressed as the effect on gas volume of a change in pressure, temperature, or amount of gas. 

The effect on gas volume of a change in pressure can be calculated by substituting values in Equation (1). 

As another example, consider the effects of a change of pressure, holding both the temperature and the number of moles constant. Calculate the new volume of a quantity of gas occupying initially 16.0 L at a pressure of 0.900 atm when the pressure is changed to 1.20 atm. In this case, both n and T remain the same and cancel out of the equation giving the following relationship ... 

Physical chemistry is concerned to a great extent with the effect that a change in one variable of a system will have on the other variables of the system. For example, how will a change in the pressure or temperature of a system affect its volume or energy Differential calculus is the mathematics of incremental changes. It is based primarily on the mathematical concept known as the derivative. The derivative of a variable y with respect to a variable jc, where y must be a function of x, is defined as... 

A gas commonly undergoes a change from an initial to a final state. Typically, you are asked to determine the effect on V, P, n, or T of a change in one or more of these variables. For example, starting with a sample of gas at 25°C and 1.00 atm, you might be asked to calculate the pressure developed when the sample is heated to 95°C at constant volume. 

Since Ag is a function of pressure, it follows that, under certain conditions, a change in pressure may produce immiscibility in a completely miscible system, or, conversely, such a change may produce complete miscibility in a partially immiscible system. The effect of pressure on miscibility in binary liquid mixtures is closely connected with the volume change on mixing, as indicated by the exact relation... 

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. 

Thus, under the influence of the field, the adsorptivity of one of the surfaces should increase, while that of the other decreases (Sec. IV,B), though not by the same amount. (This fact can be demonstrated and is highly essential.) As a result, the adsorptivity of the sample as a whole should change. This effect might be detected by a change in pressure in the adsorption volume. At the same time, the catalytic activity of the sample should also change. One may expect a change in the reaction rate under the influence of the external field. 

A gas may be defined as a homogeneous fluid of low density and low viscosity, which has neither independent shape nor Volume but expands to fill completely the vessel in which it is contained. The properties of gases differ considerably from the properties of liquids, mainly because the molecules in gases are much farther apart than molecules in liquids. For instance, a change in pressure has a much greater effect on the density of a gas than of a liquid. 

A change in pressure of only 15 bar increased the rate constant by an order of magnitude, because the density and thus the solvent strength increased significantly. This solvent effect can be explained in an alternative but more complex manner by using transition state theory. For a unimolecular reaction, A = A products, the activation volume may be expressed as... 

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