Involving Volume

The conversion factors previously noted convert from one unit of a given measure to another unit of the same measure, such as from length to length. We also have conversion factors that convert from one measure to a different one. The density of a substance, for example, can be treated as a conversion factor between mass and volume. Suppose we want to know the mass in grams of 2 cubic inches (2.00 in. ) of gold, which has a density of 19.3 g/cm. The density gives us the conversion factors  

Because we want a mass in grams, we use the first factor, which has mass in grams in the numerator. To use this factor, however, we must first convert cubic inches to cubic 

Notice that both the numbers and the units are cubed. Also, because 2.54 is an exact number, we can retain as many digits of (2.54) as we need. We have used four, one more than the number of digits in the density (19.3 g/cm ). Applying our conversion factors, we can now solve the problem  

The procedure is diagrammed here. The final answer is reported to three significant figures, the same number of significant figures as in 2.00 in. and 19.3 g. 

How many liters of water do Earth s oceans contain  

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Those involving volume approximations. We replace njVi by Vj and identify the latter as the total volume of the solution. For dilute solutions these do not introduce serious errors and do simplify the notation somewhat. 

Disposal Discharge of wastes to air, water or land in properly controlled, or safe, ways such that compliance is achieved. Secure land disposal may involve volume reduction, encapsulation, leachate containment and monitoring techniques a c j 5 j ... 

Technical Observations. In large scale operations, involving volumes of 4000 to 5000 liters, the crystallization of 2,2 -benzidinedisulfonic acid requires at least 3 days. In order to obtain rapid cooling, lead coils, through which cold water is circidated, are installed in the wooden vats. The sulfonic acid must be diazotized indirectly because of its insolubility. It is dissolved in the required amount of water and soda, the neutral solution is mixed with sodium nitrite, and the mixture is allowed to flow in a thin stream into hydrochloric or sulfuric acid. 

The volume ratios that correspond to mole ratios involve volumes of separate gas samples at the same temperature and pressure. In gas mixtures, the partial pressure ratios are equal to the mole ratios. 

Thermomechanical analysis (TMA). In this technique, information on changes in the size of a sample is obtained, e.g. thermal expansion and coefficient of thermal expansion, cure shrinkage, glass transition, thermal relaxations, any phase transformation involving volume change in the material. We describe the measurement of the coefficient of thermal expansion in detail later in this section. 

State Charles s law, and use it to solve problems involving volume and temperature. 

The relationship AH = AE + P AV is valid for any process that takes place at constant temperature and pressure. It is very useful for physical changes that involve volume changes, such as expansion or compression of a gas. When a chemical reaction occurs and causes a change in the number of moles of gas, it is more convenient to use the relationship in the form AH = AE + (An)RT. You should always remember that An refers to the change in number of moles of gas in the balanced chemical equation. 

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. 

Review of Traditional Rate Expressions Involving Volume Expansion. 

Similarly easy revisions apply to other forms of rate expressions involving volume expansion. These formulas do not require any assumption about linearity of volume expansion with conversion, nor are they invalidated by the presence of parallel or consecutive reactions. One simply needs to establish the instantaneous values of 8 at each analysis, a matter made simple if inerts are present in the feed or by calculating 5 from the P vector. 

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