Changes in Volume and Pressure

If we were to start with a gaseous system at equilibrium in a cylinder with a movable piston, we conld change the volnme of the system, thereby changing the concentrations of the reactants and prodncts. 

At 25°C the equilibrium constant for this reaction is 4.63 X 10 . Suppose we have an equilibrium mixture of 0.643 MN2O4 and 0.0547 MNO2 in a cylinder fitted with a movable piston. If we push down on the piston, the equilibrium will be disturbed and will shift in the direction that minimizes the effect of this disturbance. Corrsider what happens to the concerttratiorrs of both species if we decrease the volrrme of the cylinder by half Both corKerttratiorrs are irritially doubled [N2O4] = 1.286 M and [NO2] = 0.1094 M If we plug the new concerttratiorrs irrto the reaction quotiertt expression, we get 

In general, a decrease in volume of a reaction vessel will cause a shift in the equilibrium in the direction that minimizes the total number of moles of gas. Conversely, an increase in volume will cause a shift in the direction that maximizes the total number of moles of gas. 

Sample Problem 15.12 shows how to predict the equilibrium shift that will be caused by a volume change. 

For each reaction, predict in what direction the equilibrium will shift when the volume of the reaction vessel is decreased. 

Figu re 15.7 The effect of a volume decrease (pressure increase) on the N204(g) 2N02(g) equilibrium. 

When volume is decreased, the equilibrium is driven toward the side with the smallest number of moles of 

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The reservoir was connected to a 2-liter bulb to render the change in volume and pressure on the reference side of the manometer negligible. The construction was of glass with Rotaflow taps that facilitated total immersion in the thermostat. The system could be pressurized with pure 02 in the range 500-2000 mm Hg, variations during runs being less than... 

In 1888, the French chemist Henri-Louis Le ChStelier discovered that there are ways to control equilibria to make reactions, including this one, more productive. He proposed what is now called Le Chatelier s principle If a stress is applied to a system at equilibrium, the system shifts in the direction that relieves the stress. A stress is any kind of change in a system at equilibrium that upsets the equilibrium. You can use Le Chatelier s principle to predict how changes in concentration, volume (pressure), and temperature affect equilibrium. Changes in volume and pressure are interrelated because decreasing the volume of a reaction vessel at constant temperature increases the pressure inside. Conversely, increasing the volume decreases the pressure. 

The reactions that proceed with changes in volume and pressure are very important. Thermal cracking proceeds at high temperatures, and many products of this process are gaseous. This means that there is a volume increase during the reaction. This dependence can be described by equation (6.13). 

Air moves in and out of the lungs due to changes in volume and pressure inside the chest cavity. Inspiration is brought about by contraction of the diaphragm and the external intercostal muscles (between the ribs). The diaphragm flattens and the ribs are pulled upwards and outwards increasing the volume of the chest cavity. The pressure inside the chest cavity drops and air is drawn in through the trachea. Expiration is normally passive... 

STEP 3 Unfold and draw lines along all folds. Label the columns as follows Changes in Concentration, Changes in Volume and Pressure, and Changes in Temperature. 

Changes in volume and pressure Consider again the reaction for making methane from by-product gases. 

Changing the volume (and pressure) of an equilibrium system shifts the equilibrium only if the number of moles of gaseous reactants is different from the number of moles of gaseous products. If the number of moles of gas is the same on both sides of the equation, changes in volume and pressure have no effect on the equilibrium. 

Addition or Removal of a Substance Changes in Volume and Pressure Changes in Temperature Catalysis... 

A different type of phase transition is known in which there is a discontinuity in the second derivative of free energy. Such transitions are known as second-order transitions. From thermodynamics we know that the change in volume with pressure at constant temperature is the coefficient of compressibility, /3, and the change in volume with temperature at constant pressure is the coefficient of thermal expansion, a. The thermodynamic relationships can be shown as follows ... 

Experimental studies indicate that the maximum explosion pressure is usually not affected by changes in volume, and the maximum pressure and the maximum pressure rate are linearly dependent on the initial pressure. This is shown in Figure 6-20. As the initial pressure is increased, a point is reached where the deflagration turns into a detonation, as shown in Figure 6-21. The spikes in the curves indicate a detonation. 

The work done by the (hydrostatic) pressure, Pjj, neglecting surface tension effects, is the product of the pressure and the change in volume and is given by... 

The melting point of a compound is the temperature at which the solid and liquid phases are in equilibrium at one atmosphere pressure is specified because the melting process involves a change in volume and is therefore pressure dependent. Since the melting point can be determined easily experimentally, it is the most commonly reported physical property for organic compounds. However, in the absence of a rigorous theory of fusion, it is one of the most difficult to predict. 

Increasing the pressure will decrease the volume, while increasing the temperature will increase the volume. Therefore, the change in volume will depend on the relative sizes of the changes in temperature and pressure. 

Boyle s law can be used to solve for changes in volume when pressure changes. The gas must be in a closed system and the temperature must remain constant. You can use Charles law to solve for changes in volume with temperature changes. This law works only in a closed system in which pressure remains constant. Gay-Lussac s law can solve problems in which the amount and volume of gas remain constant while the temperature and pressure change. 

Lyon (5) proposed that A H may be affected by vacancy concentration, which varies from 14 to 15% (5) in samples of stoichiometric B-TiO obtained at normal pressure. Samples with vacancy concentrations dow to 0% have been prepared (6) at high pressure. PVT data (6) allowed calculation (5) of values of A H for Ti0(B, 0% vacancies) + TiO(B, 14% vacancies). These values, if valid, suggest that A H should be quite different for vacancy-free B-TiO and significantly different even for the normal range of vacancy concentrations. Ideal ordered a-TiO, containing 1/6 or 16.7% vacancies, should involve additional changes in volume ( ) and AjH . In summary, the discrepancy in a H may arise from sample differences - phase, composition and vacancy concentration - or from bias in the reaction calorimetry. 

This is also a good place to review the concept of standard temperature and pressure. Because the volume of a gas is so susceptible to changes in temperature and pressure, you must always make note of the temperature and pressure conditions that the volume of the gas refers to. As you should recall from Chapter 7, if you collected a 2.50 L sample of a gas in your laboratory on a day when the temperature is low and the atmospheric pressure is... 

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