Pressure, Temperature and Volume

Gases have weaker attractive forces between individual molecules and therefore diffuse rapidly and assume the shape of their container. Molecules can be separated by vast distances unless the gas is subjected to high pressure. Their volumes are easily affected by temperature and pressure. The behaviour of any gas is dependent on only a few general laws based upon the properties of volume, pressure and temperature as discussed in Chapter 4. 

T, (f), are called the reduced pressure, the reduced volume, and the reduced temperature, respectively, and equation (1) may be stated in the form that if we know the critical volume, critical pressure, and critical temperature of a substance, and divide the values of the volume, pressure, and temperature in a series of states by these, the quotients will satisfy an equation which does not contain any constants depending on the specific nature of the substance, this being in fact the equation ... 

Entropy S like internal energy, volume, pressure, and temperature is a fundamental property of a system. As such, it is a function of the state of the system and a state function so that... 

For plan 32, the purchaser will specify the fluid characteristics, and the vendor shall specify the volume, pressure, and temperature required. 

An engine operates on an Otto cycle with a compression ratio of 8. At the beginning of the isentropic compression process, the volume, pressure, and temperature of the air are 0.01 m, llOkPa, and 50°C. At the end of the combustion process, the temperature is 900°C. Find (a) the temperature at the remaining two states of the Otto cycle, (b) the pressure of the gas at the end of the combustion process, (c) the heat added per unit mass to the engine in the combustion chamber, (d) the heat removed per unit mass from the engine to the environment, (e) the compression work per unit mass added, (f) the expansion work per unit mass done, (g) MEP, and (h) thermal cycle efficiency. 

The nonadsorbed gas is pumped out and replaced by the adsorbate. Its volume, pressure, and temperature are measured, and from these the number of moles of gas introduced (initially) into the apparatus can be determined. 

We will be concerned with three variables pressure, temperature, and volume. Pressure and temperature are imposed on the system and determine the phase or phases which exist. The phases which exist are identified by their specific volumes or densities. 

For the appropriate values of volume, pressure, and temperature, the gas becomes a liquid, and according to the phase diagram of ( ee Figure 20.12), a transition from the gaseous to the solid state is possible too. As discussed earlier (see Figures 20.13 and 20.14), a distinction between an amorphous solid and a liquid is difLcult. Figure 20.15 shows the pressure-punch displapei ient (... 

Diam. diameter of the nozzle orifice A/q initial mass of cocoa butter Vs, Ip, T5 volume, pressure and temperature of the tank (5), respectively P7, 7 7 pressure and temperature of the tank (7), respectively. 

The individual gas laws can be used to derive a law involving all three influencing factors—volume, pressure, and temperature—into one law. Since the three laws deal with a fixed amount of gas (no change in mass), so does... 

Later chemists added temperature to the equation, and by the middle of the nineteenth century, scientists had developed the ideal gas law. An ideal gas is a hypothetical gas in which the molecules (or atoms) themselves occupy no volume and there is no attraction between molecules. The law can be written as an equation relating the volume, pressure, and temperature of such a gas. 

Final Directions Wash the whole apparatus free from acid. Preserve the platinum wire for future use. If the final result is incorrect, first examine the arithmetical work, then repeat the readings (gas volume, pressure, and temperature), and recalculate, if blunders were made. 

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. 

Many applications in chemistry require us to interpret—and even predict—the results of measurements where we have only limited information about the system and the process involved. In such cases the best we can do is identify the possible outcomes of the experiment and assign a probability to each of them. Two examples illustrate the issues we face. In discussions of atomic structure, we would like to know the position of an electron relative to the nucleus. The principles of quantum mechanics tell us we can never know the exact location or trajectory of an electron the most information we can have is the probability of finding an electron at each point in space around the nucleus. In discussing the behavior of a macroscopic amount of helium gas confined at a particular volume, pressure, and temperature we would like to know the speed with which an atom is moving in the container. We do not have experimental means to tag a particular atom. 

Chapter 4 the types of compounds Chapter 5 naming compounds writing chemical formulas Chapter 6 writing and balancing chemical reactions Chapter 10 the factor label method volume, pressure, and temperature relationships of gases... 

Stoichiometry deals with calculations based on balanced chemical equations (see Chapter 8). Recall how the coefficients in a balanced equation correspond to the number of moles of each species in the equation. For gases in a balanced equation, the ideal gas law conveniently relates moles of a gas to its volume, pressure, and temperature. 

The state of a given amount of a gas is specified by its volume, pressure, and temperature. Consider a gas at 2 atm, 300 K, and 1 L (the initial state). Suppose a process is carried out at constant temperature such that the gas pressure decreases to 1 atm. According to Boyle s law, its volume must increase to 2 L. The final state then corresponds to 1 atm, 300 K, and 2 L. The change in volume (AV) is... 

State of a system. The values of all pertinent macroscopic variables (for example, composition, volume, pressure, and temperature) of a system. (6.7) Stereoisomers. Compounds that are made up of the same types and numbers of atoms bonded together in the same sequence but with different spatial arrangements. (22.4) Stoichiometric amounts. The exact molar amounts of reactants and products that appear in the balanced chemical equation. (3.9)... 

Often, a sample of gas (a fixed number of moles of gas) undergoes change involving volume, pressure, and temperature simultaneously. It would be useful to have one equation that describes such processes. 

An excellent study of the relation between hydrocarbon structure and compressibility was carried out by Cutler, McMickle, Webb and Schiessler [41]. The modification of Bridgman s method used to determine the compressibilities is described well and the specific volume data are given in detail over a pressure range from atmospheric to 1 GPa (10,000 bars) and a temperature range from 311.0 to 408.2 K (37.8 to 135 C). No attempt was made to develop a three-variable equation of state relating volume, pressure and temperature however, the pressure-volume isotherms were examined analytically with respect to the Tait equation ... 

In Chapters 3 and 4, we encountered many reactions that involved gases as reactants (e.g., combustion with O2) or as products (e.g., a metal displacing H2 from acid). From the balanced equation, we used stoichiometrically equivalent molar ratios to calculate the amounts (moles) of reactants and products and converted these quantities into masses, numbers of molecules, or solution volumes (see Figure 3.10). Figure 5.11 shows how you can expand your problem-solving repertoire by using the ideal gas law to convert between gas variables (F, T, and V) and amounts (moles) of gaseous reactants and products. In effect, you combine a gas law problem with a stoichiometry problem it is more realistic to measure the volume, pressure, and temperature of a gas than its mass. 

An important point to understand is that there is no partieular sequenee by whieh the internal energy (E) of a system must change. This is because is a state function, a property dependent only on the current state of the system (its composition, volume, pressure, and temperature), not on the path the system took to reach that state the current state depends only on the difference between the final and initial states. As an analogy, the balance in your checkbook is a state function of your personal financial system. You can open a new account with a birthday gift of 50, or you can open a new account with a deposit of a 100 paycheck and then write two 25 checks. The two paths to the balance are different, but the balance (cunent state) is the same. And you can imagine countless other paths to the same balance. 

You are given the volume, pressure, and temperature of a gas sample. The mole and volume ratios of gaseous reactants and products are given by the coefficients in the balanced chemical equation. Volume can be converted to moles and thus related to mass by using molar mass and the ideal gas law. 

Equation (7-12) is a special case of the law of corresponding states which predicts that equations of state of all normal substances are the same, if the volume, pressure, and temperature are expressed in terms of their respective values for some unique point in the equation, such as the critical point. Any equation of state which contains two constants characteristic of the gas can be cast into such a form that the law of corresponding states applies. 

We know the initial volume, pressure, and temperature of both gases. 

Here is a useful leisure time exercise for a very attentive reader. The purpose is to understand the connection between virial expansion (8.7) and the well known van der Waals equation of state (i.e., the relationship between volume, pressure, and temperature) for an ordinary imperfect gas. You may have studied van der Waals equation in general physics and/or general chemistry class, it reads p- -a/V )(V — b) = NksT. Say, the volume is V, and the number of molecules in the gas is N. Then n = N/V. You can work out the pressure by differentiation p = — (9F/9V), where free energy F is defined by formula (7.19), F = U — TS = t/ + / , the internal energy U is given by (8.7), and... 

Analyze This is a multistep problem. We are given the volume, pressure, and temperature of the N2 gas and the chemical equation for the reaction by which the N2 is generated. We must use this information to calculate the number of grams of NaN3 needed to obtain the necessary N2. 

We discuss Le Chatelier s principle, which predicts how a system at equilibrium responds to changes in concentration, volume, pressure, and temperature. 

The relationship between volume, pressure, and temperature is represented graphically by a three-dimensional surface whose general shape is shown in Figure 2-1. This graph has been rotated to show pressure in the vertical axis, with the mesh lines on the surface representing lines of constant temperature... 

This relationship exists between any three variables that are related by an equation. Since volume, pressure, and temperature are related via the equation of state, we obtain the following result as an immediate consequence of the triple-product rule ... 

A Figure 10.9 Avogadro s hypothesis. At the same volume, pressure, and temperature, samples of different gases have the same number ot molecules but different masses. 

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