Volume amount-mass-number relationships

Figure 3.9 Summary of amount-mass-number relationships in solution. The amount (mol) of a substance in solution is related to the volume (L) of solution through the molarity (M mol/L). As always, convert the given quantity to amount (mol) first.

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

The number of moles is a fourth variable that can be added to pressure, volume, and temperature as a way to describe a gas sample. Recall that as the other gas laws were presented, care was taken to state that the relationships hold true for a fixed mass or a given amount of a gas sample. Changing the number of gas particles present will affect at least one of the other three variables. 

Molarity can be thought of as a conversion factor used to convert between volume of solution and amount (mol) of solute, from which we then find the mass or the number of entities of solute. Figure 3.10 (on the next page) shows this new stoichiometric relationship, and Sample Problem 3.13 applies it. 

Equation of state (EOS) n. For an ideal gas, if the pressure and temperature are constant, the volume of of the gas depends on the mass, or amount of gas. Then, a single property called the gas density (ratio of mass/volume). If the mass and temperature are held constant, the product of pressure and volume are observed to be nearly constant for a real gas. The product of pressure and volume is exactly for an ideal gas. This relationship between pressure and volume is called Boyle s Law. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay-Lussac s law. The gas laws of Boyle and Charles and Gay-Lussac can be combined into a single equation of state PV = nRT, where P is pressure, V volume, Tabsolute temperature, n number of moles and R is the universal gas constant. Ane-rodynamicists us a different form of the equation of state that is specialized of air. Regarding polymers and monomers, equation of state is an equation giving the specific volume (v) of a polymer from the known temperature and pressure and, sometimes, from its morphological form. An early example is the modified Van der Waals form, successfully tested on amorphous and molten polymers. The equation is ... 

In Chapter 0, we used relationships between amounts (in moles) and masses (in grams) of reactants and products to solve stoichiometry problems. When the reactants and/or products are gases, we can also use the ideal gas equation to relate the number of moles n to the volume V or pressure P to solve such problems. Examples 5.7 and 5.8 show how the ideal gas equation is used in such calculations. 

Figure 3.10 Suminary of mass-mole-number-volume relationships in solution. The amount (in moles) of a compound in solution is related to the volume of solution in liters through the rmlarity 0M) in moles per liter. The other relationships shown are identical to those in Figure 3.4, except that here they refer to the quantities in solution. As in previous cases, to find the quantity of substance expressed in one form or another, convert the given information to moles first...

The relationships between the number of metric units and the number of USCS units are direct proportionalities. You may find it useful to memorize only one conversion in each of three categories mass, length, and volume. You can then use familiar metric-metric and/or USCS-USCS conversions to change units within each system of measurement. Although it can add a few steps to a problem, this approach minimizes the amount of memorization necessary. 

STRATEGIZE Since the reaction occurs under standard temperature and pressure, you can convert directly from the volume (in L) of hydrogen gas to the amount in moles. Then use the stoichiometric relationship from the balanced eqnation to find the number of moles of water formed. Finally, use the molar mass of water to obtain the mass of water formed. 

---