Molecules in 1 mole

You should recall from the review of the mole unit that the reaction coefficients (2, 1, and 2 in the preceding example) can be interpreted as molecules, or as moles, or as volumes. This is because Avogadro s law holds for all gases. The number of molecules in 1 mole of a gas is known to be... 

The racemization of an amino acid provides a biochemical example that can be related directly to Eq. 6-9. A solution of an L-amino acid will be efficiently changed into the racemic mixture of 50% d and 50% l by the action of an enzyme (a racemase) with no uptake or evolution of heat. Thus, AH = 0 and the only change is an entropy change. Let us designate 2 for the pure isomer as 2. Since there are just two choices of configuration for each of the N molecules in 1 mole of the racemate we see that for the racemate... 

If N is of the order of 6 X 10, the number of molecules in 1 mole of a gas, the probability becomes (2) ° which is such a small number that, for all practical purposes, it can be regarded as zero. On the basis of probability considerations, we would expect the gas to fill both flasks spontaneously and evenly. By the same token, we now understand that the situation depicted in Figure 18.1(b) is not spontaneous because it represents a highly improbable event. To summarize our discussion An ordered state has a low probability of occurring and a small entropy, while a disordered state has a high probabihty of occurring and a large entropy. 

One gram-molecular weight (abbreviation mole or mol) of any compound is a mass of that compound equal to its molecular weight in grams. Thus, 1 mole of water is 18.015 g of water. One mole of any compound contains the same number of molecules as one mole of any other compound. The number of molecules in 1 mole of any compound is 6.022 X 10 which is called Avogadro s number (A /v) Since the volume occupied by a gas depends on its temperature, pressure, and the number of molecules in the gas, at the same temperature and pressure 1 mole of the gas of any compound occupies the same volume as 1 mole of the gas of any other compound. At standard temperature and pressure (STP), which are defined as 0°C and 1 bar (=10 Pa), the volume occupied by 1 mole of any gas is about 22.4 L. 

Answer The Avogadro number is the number of molecules in 1 mole of a gas (22.4 liters at sc). From Example 3, this is... 

As in a previous case, the genera number of adsorbed initial molecules is 1 mole. If intermolecular bonds are great enough, molecules in the volume cannot transit, and there is no motion at the surface. In this case, we can omit terms connected with combinatorial entropy of molecule disposition in the volume, and, even more so, their difference ... 

Once you know the mass or number of molecules in 1 mol, you merely have to multiply to get the mass or number of molecules in any other given number of moles. Sometimes the calculation is easy enough to do in your head. 

Assuming air has an average molar mass of 28.8 grams/mole, show how there are 0.0410 moles of air molecules in 1 liter of air. (See Section 9.2 for a review of this calculation.)... 

The mole (mol) is simply a unit of quantity, it represents a certain amount of material, i.e. atoms or molecules. The numerical value of one mole is 3 23 x 1023 and is referred to as Avogadro s number. The mole is defined iis/the mass, in grams, equal to the atomic mass of an element or molecule. Therefore, 1 mole of carbon weighs 12 grams and contains 6.023 x 1023 carbon atoms. The following formula can be used to find the number of moles ... 

Remember that kinetic energy is 1/2mv1. The Boltzmann constant k is equal to the ideal gas constant R divided by Avogadro s number. Avogadro s number is the number of molecules in a mole, so the Boltzmann constant treats individual molecules, while the ideal gas constant deals with moles of molecules. So, if we use the molecular mass (M), we need to use the ideal gas constant. Also, we re always safest in physics when we stick to SI units, so let s express the molecular mass in units of kg/mol and R in units of J/mol/K. So, on a molar scale, we can recast the relationship between kinetic energy and temperature as ... 

No being Avogadro s number, the number of molecules in a mole, given in Eq. (3.10) of Chap. IV. We observe that Eq. (3.14) is exactly the same as (1.21), determined by thermodynamics, except that now we have found the quantities Uo, the arbitrary constant in the energy, and i, the chemical constant, in terms of atomic constants. Similarly, we can show that all the other formulas of Sec. 1 follow from our statistical mechanical methods, using Eqs. (3.15) and (3.16) for the constants which could not be evaluated from thermodynamics. 

It would be of interest to have an idea of the path of such a gas molecule in the course of time. One might think that the detailed paths of all the particles could be predicted by applying Newton s laws to the motions of molecules. The problem, however, is obviously too complex for a practical solution. To use the laws ofmotion requires a knowledge of the position and velocity of each particle and even in 1 mole there are 6.023 x 10 (the Avogadro number) particles. 

Perhaps you still can t picture the size of a 6 ml sample of water. Think, instead, of a 1-liter bottle of water. Let s calculate the number of moles of water molecules in 1 liter of water. One liter is equal to 1000 ml. We already said that one mole of water occupies about 18 ml. We need to divide 1000 ml by 18 ml to determine how many moles of water molecules there are in one liter of water. Let s solve the problem using the factor-label method, which you ll remember from Chapter 2. 

To add to this convenience, the number 602,000,000,000,000,000,000,000 is also given a name. It is called Avogadro s number, in honor of Amedeo Avogadro, a famous Italian chemist. So, if you are speaking about the total number of atoms in 1 mole of water molecules, you can simply say three times Avogadro s number, or 3 x (6.02 x 1023), which is 1.81 x 104 atoms. 

How many atoms can be found in 1 mole of water (HzO) molecules ... 

Whether you are dealing with elements or compounds, the molar mass of a species is the mass in grams of 1 mole (6.022 x 1023) of that species 1 mole of atoms, 1 mole of molecules, or 1 mole of formula units. With compounds, you re dealing with molecules and formula units, so it is necessary to calculate the molecular or formula mass of each compound to get its molar mass. It s easy to get confused by the language ... 

It is important to keep in mind that molarity refers only to the amount of solute originally dissolved in water and does not take into account any subsequent processes, such as the dissociation of a salt or the ionization of an acid. Both glucose and urea are nonelectrolytes, so a 1.00 M urea solution has 1.00 mole of the urea molecules in 1 liter of solution. But consider what happens when a sample of potassium chloride (KCl), a strong electrolyte, is dissolved in enough water to make a 1 M solution ... 

This equation tells us that breaking the covalent bonds in 1 mole of gaseous H2 molecules requires 436.4 kJ of energy. For the less stable chlorine molecule. 

The energy changes are sketched in Figure 2- 28. We are looking at the case where 1 mole of lithium atoms reacts with a F2 mole of fluor gas molecules and 1 mole of solid lithium fluoride is formed. 

You need to apply equation (1,6). Remember that you need to convert the temperature ( C) to absolute temperature and that there are 6.023 X 1023 molecules in one mole. 

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