Moles of molecules

Given the partition functions, the enthalpy and entropy terms may be calculated by carrying out the required differentiations in eq. (12.8). For one mole of molecules, the results for a non-linear system are (R being the gas constant)... 

Consider the substance hydrogen chloride. This compound has the molecular formula HQ. A chemist working with hydrogen chloride, HQ, must often know the weight of a mole of molecules (the molecular weight). This weight is readily calculated from the atomic weights of the two kinds of atoms, H and Cl ... 

We will use equation (10.70) to calculate the energy difference for one mole, where N = NA, Avogadro s number and Z = Zm, the partition function for a mole of molecules. Equation (10.70) then becomes... 

FIGURE 2.18 The bond dissociation energies of the hydrogen halide molecules in kilojoules per mole of molecules. Note how the bonds weaken as the halogen atom becomes larger. 

Avogadro s principle is commonly expressed in the terms of the molar volume, Vm, the volume occupied per mole of molecules ... 

STRATEGY We convert from the given volume of gas into moles of molecules (by using the molar volume), then into moles of reactant molecules or formula units (by using a mole ratio), and then into the mass of reactant (by using its molar mass). If the molar volume at the stated conditions is not available, then use the ideal gas law to calculate the amount of gas molecules. 

The easiest way to express the relation between the total pressure of a mixture and the partial pressures of its components is to introduce the mole fraction, x, of each component A, B,. . ., the number of moles of molecules of the gas expressed as a fraction of the total number of moles of molecules in the sample. If the amounts of gas molecules present are nA, B, and so forth, the mole fraction of A is... 

Next, we express the total pressure in terms of n, the total number of moles of molecules present ... 

The temperature-independent van der Waals parameters a and b are unique for each gas and are determined experimentally (Table 4.5). Parameter a represents the role of attractions so it is relatively large for molecules that attract each other strongly and for large molecules with many electrons. Parameter b represents the role of repulsions it can be thought of as representing the volume of an individual molecule (more precisely, the volume per mole of molecules), because it is the repulsive forces between molecules that prevent one molecule from occupying the space already occupied by another molecule. 

A note on good practice You should always be alert to the difference between a quantity per mole of molecules and the same quantity for or of a mole of molecules. Standard enthalpies of formation are expressed per mole of molecules, as in —277.69 kj-mol the standard enthalpy of forming 1 mol C2H5OH(l) is —277.69 kj. The point might seem picky, but it will help you to keep units straight. 

The entropy of vaporization, ASvap, is the change in entropy per mole of molecules when a substance changes from a liquid into a vapor. The heat required per mole to vaporize the liquid at constant pressure is equal to the enthalpy of vaporization (A//vap, Section 6.11). It then follows from Eq. 1, by setting = AH, that the entropy of vaporization at the normal boiling point is... 

Using data available in Appendix 2A, write balanced equations and calculate the hear released when (a) 1.00 mol and (b) 1.00 g of each of the following compounds is burned in excess oxygen propane, butane, and pentane. Is there a trend in the amount of heat released per mole of molecules or per gram of compound If so, what is it ... 

Thus, we need the mass (m) in kilograms. The molar mass gives the mass of one mole of molecules, so dividing molar mass by Avogadro s number (A ji) gives the mass per molecule ... 

The gas laws work with moles of molecules, not atoms. It is necessary to know that hydrogen gas occurs in diatomic molecules so that the proper number of moles of gas may be calculated from the mass of the gas. 

To calculate the relative molecular mass of one mole of molecules of a substance, add up the relative atomic masses of the constituent elements. 

Equation (9.55) is the expression for the entropy of mixing of polymer solutions introduced first by Flory [7], Nm and iVp can be related through x m + Xp = 1, which for one mole of molecules (polymers + monomers) gives... 

A concept strictly related to the Avogadro Number (NA) is that of mole . It is the amount unit of a substance and it is defined as an NA of entities (to be specified, if not clearly implied). A mole of atoms of 12C, for instance, corresponds by definition, to Na atoms of 12C that is to 12 g of 12C. Similarly a mole of atoms of oxygen (15.9994 g) corresponds to NA atoms of oxygen and a mole of molecules of oxygen (31.9988 g of oxygen) corresponds to NA molecules 02 and as a final example,... 

Note that the terms macroscopic and microscopic constants do not imply that these quantities measure macroscopic or microscopic quantities, respectively. Here, in the macroscopic view we have simply grouped the two microscopic species (0, 1) and (1, 0) into one species denoted by (1). Both of these constants can be macroscopic or microscopic, depending on whether we study the binding per molecule or per one mole of molecules. 

This is the mcvcimumpossible rate ojbimolecular reaction, the collision rate of the molecules that can react. We must multiply this by a probability of reaction in the collision so actual rates must be less than this. We know that the units of k should be Uters/mole time, and, since velocity is in lengthAime and cross section is in area/time, the units are correct if we make sure that we use volume in liters, and compute the area of a mole of molecules. If the molecular weight is 28 (air) and the temperature is 300 K, then we have... 

A second consequence of the ideal gas assumption is that PV in Eq. (10.4) may be replaced by Nk T. In the special case where we are working with one mole of molecules, in which case N = (Avogadro s number), we may replace PV with RT, where R is tlie universal gas constant (8.3145 J moV K ). 

The term "mole" commonly is used to represent the number of molecules (or atoms) in a quantity of material that is, one mole of molecules = Avogadro s number of molecules. In this sense, a mole is a dimensionless number, just as a dozen means 12. For example, you could talk about a mole of caterpillars,... 

Many of these effects of radioactive decay can be treated quantitatively using G values. Historically, the G value was defined as the number of molecules or species decomposed or formed per 100 eV of absorbed energy. A newer (SI) definition of the G value is the number of moles of molecules or species formed or decomposed per Joule of energy absorbed. (Note that 1 mol/J = 9.76 x 106 molecules/100 eV.) The G values depend on the radiation and the medium being irradiated and its physical state. Table 19.1 shows some typical G values for the irradiation of neutral liquid water. 

There are two commonly used and numerically different ways of expressing the average molecular weight of a polymer such as polycyclopentadiene. One is the number-average molecular weight, M, which is the total weight of a polymer sample, m, divided by the total number of moles of molecules it contains, SAT Thus... 

Once the molar mass of a compound has been calculated, the same technique applied in Example E.2 can be used to determine how many moles of molecules or formula units are in a sample of a given mass. 

The mole fraction of a substance in a mixture is its number of moles expressed as a fraction of the total number of moles of molecules in the mixture. 

A third contribution to our understanding of gases was made by the Italian scientist Amedeo Avogadro, whose work enabled scientists to accept the reality of atoms. The molar volume, VJm of a substance—any substance, not only a gas—is the volume it occupies per mole of molecules, n. Specifically, if V is the volume of a sample and n is the number of moles of molecules the sample contains, the molar volume is... 

Because Vm is a constant at constant temperature and pressure, this expression tells us that doubling the number of moles of molecules at constant temperature and pressure doubles the volume occupied by a gas. This behavior is consistent with our model of gases. In this model, gas molecules are in constant motion and beat against the walls of their container. To keep the pressure constant as more molecules are added, the size of the container must increase. 

The volume occupied by a sample of gas at constant pressure and temperature is directly proportional to the number of moles of molecules present V °c n. 

Self-Test 4.6B A 10.0-mol sample of gas in an industrial reactor of fixed volume must be kept at a constant pressure of 5.00 atm. As the tank is heated, the temperature rises from an initial 25°C to a final 300°C. To maintain the pressure, the engineer releases some of the gas through a safety t valve. How much gas (in moles of molecules) must be released to maintain the constant pressure ... 

The ideal gas law, p V = nRT, is an equation of state that summarizes all the relations describing the response of an ideal gas to changes in pressure, volume, temperature, and moles of molecules it is an example of a limiting law. 

The molar concentration of a gas and a related quantity, the density of a gas, are both of great interest to meteorologists as well as to engineers. As we saw in Section G, the molar concentration is the number of moles of molecules divided by the volume of the sample (n/V). It follows from the ideal gas law that, for a gas behaving ideally,... 

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