# Measures of Concentration

Solutions are often described in terms of their concentration—how much solute is present in a given volume of solution. Concentration is expressed in different ways for different purposes, some of which are explained here. You may find the table of symbols and measures inside the back cover to be helpful as you study this section.

### Weight per Volume

A simple way to express concentration is the weight of solute in a given volume of solution. For example, intravenous (I.V.) saline typically contains 8.5 grams of NaCl per liter of solution (8.5 g/L). For many biological purposes, however, we deal with smaller quantities such as milligrams per deciliter (mg/dL; 1 dL = 100 mL). For example, a typical serum cholesterol concentration may be 200 mg/dL, also expressed 200 mg/100 mL or 200 milligram-percent (mg-%).

### Percentages

Percentage concentrations are also simple to compute, but it is necessary to specify whether the percentage refers to the weight or the volume of solute in a given volume of solution. For example, if we begin with 5 g of dextrose (an isomer of glucose) and add enough water to make 100 mL of solution, the resulting concentration will be 5% weight per volume (w/v). A common intravenous fluid is D5W, which stands for 5% w/v dextrose in distilled water. If the solute is a liquid, such as ethanol, percentages refer to volume of solute per volume of solution. Thus, 70 mL of ethanol diluted with water to 100 mL of solution produces 70% volume per volume (70% v/v) ethanol.

### Molarity

Percent concentrations are easy to prepare, but that unit of measurement is inadequate for many purposes. The physiological effect of a chemical depends on how many molecules of it are present in a given volume, not the weight of the chemical. Five percent glucose, for example, contains almost twice as many glucose molecules as the same volume of 5% sucrose (fig. 2.11a). Each solution contains 50 g of sugar per liter, but glucose has a molecular weight (MW) of 180 and sucrose has a MW of 342. Since each molecule of glucose is lighter, 50 g of glucose contains more molecules than 50 g of sucrose.

To produce solutions with a known number of molecules per volume, we must factor in the molecular weight. If we know the MW and weigh out that many grams of the substance, we have a quantity known as its gram molecular weight, or 1 mole. One mole of glucose is 180 g and 1 mole of sucrose is 342 g. Each quantity contains the same number of molecules of the respective sugar—a number known as Avogadro's9 number, 6.023 X 1023. Such a large number is hard to imagine. If each molecule were the size of a pea, 6.023 X 1023 molecules would cover 60 earth-sized planets 3 m (10 ft) deep!

Molarity (M) is the number of moles of solute per liter of solution. A one-molar (1.0 M) solution of glucose contains 180 g/L, and 1.0 M solution of sucrose contains 342 g/L. Both have the same number of solute molecules in a given volume (fig. 2.11b). Body fluids and laboratory solutions usually are less concentrated than 1 M, so biologists and clinicians more often work with millimolar (mM) and micromolar (^M) concentrations—10~3 and 10~6 M, respectively.

Electrolyte Concentrations

Electrolytes are important for their chemical, physical (osmotic), and electrical effects on the body. Their electri-

 Table 2.4 Types of Mixtures Solution Colloid Suspension Particle size < 1 nm 1-100 nm >100 nm Appearance Clear Often cloudy Cloudy-opaque Will particles settle out? No No Yes Will particles pass through a selectively permeable membrane? Yes No No Examples Glucose in blood Proteins in blood Blood cells O2 in water Intracellular fluid Cornstarch in water Saline solutions Milk protein Fats in blood Sugar in coffee Gelatin Kaopectate

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Figure 2.11 Comparison of Percentage and Molar Concentrations. (a) Solutions with the same percentage concentrations can differ greatly in the number of molecules per volume because of differences in molecular weights of the solutes. Fifty grams of sucrose has about half as many molecules as 50 g of glucose, for example. (b) Solutions with the same molarity have the same number of molecules per volume because molarity takes differences in molecular weight into account.

Figure 2.11 Comparison of Percentage and Molar Concentrations. (a) Solutions with the same percentage concentrations can differ greatly in the number of molecules per volume because of differences in molecular weights of the solutes. Fifty grams of sucrose has about half as many molecules as 50 g of glucose, for example. (b) Solutions with the same molarity have the same number of molecules per volume because molarity takes differences in molecular weight into account.

cal effects, which determine such things as nerve, heart, and muscle actions, depend not only on their concentration but also on their electrical charge. A calcium ion (Ca2+) has twice the electrical effect of a sodium ion (Na+), for example, because it carries twice the charge. When we measure electrolyte concentrations, we must therefore take the charges into account.

One equivalent (Eq) of an electrolyte is the amount that would electrically neutralize 1 mole of hydrogen ions (H+) or hydroxide ions (OH-). For example, 1 mole (58.4 g) of NaCl yields 1 mole, or 1 Eq, of Na+ in solution. Thus, an NaCl solution of 58.4 g/L contains 1 equivalent of Na+ per liter (1 Eq/L). One mole (98 g) of sulfuric acid (H2SO4) yields 2 moles of positive charges (H+). Thus, 98 g of sul-furic acid per liter would be a solution of 2 Eq/L.

The electrolytes in our body fluids have concentrations less than 1 Eq/L, so we more often express their concentrations in milliequivalents per liter (mEq/L). If you know the millimolar concentration of an electrolyte, you

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can easily convert this to mEq/L by multiplying it by the valence of the ion:

1 mM Na+ = 1 mEq/L 1 mM Ca2+ = 2 mEq/L 1 mM Fe3+ = 3 mEq/L