Concentration of Solutions

The term concentration refers to the amount of solute dissolved into the solvent. Concentration can be described either qualitatively or quantitatively. Calling something a dilute solution is an example of a qualitative description. Stating that a specific container holds 50 ml of 0.4 molar solution of sodium hydroxide (NaOH) is a quantitative description (Figure 12-1, A). Saturated solutions occur when the solvent has dissociated the maximal amount of solute into itself. Additional solute added to a saturated solution does not dissociate into solution but remains at the bottom of the container (see Figure 12-1, B). Solute particles precipitate into the solid state at the same rate at which other particles go into solution. This equilibrium characterizes a saturated solution.

A solution is characterized as being supersaturated when the solvent contains more solute than a saturated solution at the same temperature and pressure. If a saturated solution is heated, the solute equilibrium is upset, and more solute goes into solution. If undissolved solute is removed and the solution is cooled gently, there is an excess of dissolved solute (see Figure 12-1, C). The excess solute of supersaturated solutions may be precipitated out if the solution is disturbed or if a “seed crystal” is introduced.

Starling Forces

Starling was a nineteenth-century British physiologist who studied fluid transport across membranes. His hypothesis states that the fluid movement secondary to filtration across the wall of a capillary depends on both the hydrostatic and the oncotic pressure gradients across the capillary.² The driving force for fluid filtration across the wall of the capillary is determined by four separate pressures: hydraulic (hydrostatic) and colloid osmotic pressure both within the vessel and in the tissue space.³ This process can be described mathematically using the following equation:

Jv=Lp [Pc−Pi−s (pc−pi)]

Where:

Osmotic Pressure of Solutions

Most of the solutions of physiologic importance in the body are dilute. Solutes in dilute solution show many of the properties of gases. This behavior results from the relatively large distances between the molecules in dilute solutions. The most important physiologic characteristic of solutions is their ability to exert pressure.

Osmotic pressure (oncotic pressure)⁴ is the force produced by solvent particles under certain conditions. A membrane that permits passage of solvent molecules but not solute is called a semipermeable membrane. If such a membrane divides a solution into two compartments, molecules of solvent can pass through it from one side to the other (Figure 12-2, A). The number of solvent molecules passing (or diffusing) in one direction must equal the number of solute molecules passing in the opposite direction. An equal ratio of solute to solvent particles (i.e., the concentration of the solution) is maintained on both sides of the membrane. A capillary wall is an example of a semipermeable membrane.^5,6

If a solution is placed on one side of a semipermeable membrane and pure solvent is placed on the other, solvent molecules move through the membrane into the solution. The force driving solvent molecules through the membrane is called osmotic pressure. Osmotic pressure tries to redistribute solvent molecules so that the same concentration exists on both sides of the membrane. Osmotic pressure may be measured by connecting a manometer to the expanding column of the solution (see Figure 12-2, B and C).

Osmotic pressure can also be visualized as an attractive force of solute particles in a concentrated solution. If 100 ml of a 50% solution is placed on one side of a membrane and 100 ml of a 30% solution is placed on the other side, solvent molecules move from the dilute to the concentrated side (see Figure 12-2, D and E). The particles in the concentrated solution attract solvent molecules from the dilute solution until equilibrium occurs. Equilibrium exists when the concentrations (i.e., ratio of solute to solvent) in the two compartments are equal (40% in Figure 12-2).

Osmolality is defined as the ratio of solute to solvent. In physiology, the solvent is water.1,5,7 Osmotic pressure depends on the number of particles in solution but not on their charge or identity. A 2% solution has twice the osmotic pressure of a 1% solution under similar pressures. For a given amount of solute, osmotic pressure is inversely proportional to the volume of solvent. Most cell walls are semipermeable membranes. Through osmotic pressure, water is distributed throughout the body within certain physiologic ranges. Tonicity describes how much osmotic pressure is exerted by a solution. Average body cellular fluid has a tonicity equal to a 0.9% solution of sodium chloride (NaCl; sometimes referred to as physiologic saline). Solutions with similar tonicity are called isotonic. Solutions with more tonicity are hypertonic, and solutions with less tonicity are hypotonic. Most cells reside in a hypotonic environment in which the concentration of water (solute) is lower inside the cell than in the surroundings. Water flows into the cell causing it to expand until the cell membrane restricts further expansion. Pressure increases inside the cell to counteract osmotic pressure. This pressure is called turgor, and it is what prevents more water from entering the cell. The equilibrium that develops allows the cell to maintain a gradient across the cell membrane. Some cells have selective permeability, allowing passage not only of water but also of specific solutes. Through these mechanisms, nutrients and physiologic solutions are distributed throughout the body.

In electrochemical terms, there are three basic types of physiologic solutions. Depending on the solute, solutions are ionic (electrovalent), polar covalent, or nonpolar covalent (Table 12-1). In ionic and polar covalent solutions, some of the solute ionizes into separate particles known as ions. A solution in which this dissociation occurs is called an electrolyte solution (Figure 12-3). If an electrode is placed in such a solution, positive ions migrate to the negative pole of the electrode. These ions are called cations. Negative ions migrate to the positive pole of the electrode; they are called anions. In nonpolar covalent solutions, molecules of solute remain intact and do not carry electrical charges; these solutions are referred to as nonelectrolytes. These nonelectrolytes are not attracted to either the positive or the negative pole of an electrode (hence the designation nonpolar). All three types of solutions coexist in the body. These solutions also serve as the media in which colloids and simple suspensions are dispersed. Gases such as O₂ and CO₂ are nonpolar molecules (along with N₂) and do not dissolve very well in water, which is a polar solvent.

Quantifying Solute Content and Activity

The amount of solute in a solution can be quantified in two ways: (1) by actual weight (grams or milligrams) and (2) by chemical combining power. The weight of a solute is easy to measure and specify. However, it does not indicate chemical combining power. The sodium ion (Na⁺) has a gram ionic weight of 23. The bicarbonate ion (HCO₃⁻) has a gram ionic weight of 61. Because the gram atomic weight of every substance has 6.023 × 10²³ particles, these ions have the same chemical combining power in solution. The number of chemically reactive units is usually more meaningful than their weight.

Equivalent Weights

In medicine, it is customary to refer to physiologic substances in terms of chemical combining power. The measure commonly used is equivalent weight. Equivalent weights are amounts of substances that have equal chemical combining power. For example, if chemical A reacts with chemical B, by definition, 1 equivalent weight of A reacts with exactly 1 equivalent weight of B. No excess reactants of A or B remain.

Two magnitudes of equivalent weights are used to calculate chemical combining power: gram equivalent weight (gEq) and milligram equivalent weight, or milliequivalent (mEq). One milliequivalent (1 mEq) is of 1 gEq.

Gram Equivalent Weight Values

A gEq of a substance is calculated as its gram molecular (formula) weight divided by its valence. Valence refers to the number of electrons that need to be added or removed to make the substance electrically neutral. The valence signs (+ or −) are disregarded.

gEq=Gram molecular weightValence

The gEq of sodium (Na⁺), with a valence of 1, equals its gram atomic weight of 23 g. The gEq of calcium (Ca⁺⁺) is its atomic weight (i.e., 40) divided by 2, or 20 g. The gEq of ferric iron (Fe⁺⁺⁺) is its atomic weight (i.e., 55.8) divided by 3, or approximately 18.6 g.

For radicals such as sulfate (SO₄²⁻), the formula for sulfuric acid (H₂SO₄) shows that one sulfate group combines with two atoms of hydrogen. Half (0.5) of a mole of sulfate is equivalent to 1 mole of hydrogen atoms. The gEq of SO₄²⁻ is half its gram formula weight, or 48 g. If an element has more than one valence, the valence must be specified or must be apparent from the observed chemical combining properties.

Gram Equivalent Weight of an Acid

The gEq of an acid is the weight of the acid (in grams) that contains 1 mole of replaceable hydrogen. The gEq of an acid may be calculated by dividing its gram formula weight by the number of hydrogen atoms in its formula, as shown in the following reaction:

HCl+Na+→NaCl+H+

The single H⁺ of hydrochloric acid (HCl) is replaced by Na⁺. In 1 mole of HCl, there is 1 mole of replaceable hydrogen. By definition, the gEq of HCl must be the same as its gram formula weight, or 36.5 g. The two hydrogen atoms of sulfuric acid (H₂SO₄) are both considered to be replaceable. In 1 mole of sulfuric acid, there are 2 moles of replaceable hydrogen, and the gEq of H₂SO₄ is half its gram formula weight, or 48 g.

Acids in which hydrogen atoms are not completely replaceable are exceptions to the rule. In some acids, H⁺ replacement varies according to specific reactions. Carbonic acid (H₂CO₃) and phosphoric acid (H₃PO₄) are examples of such exceptions. Their equivalent weights are determined by the conditions of their chemical reactions.

For example, H₂CO₃ has two hydrogen atoms. In physiologic reactions, only one is considered replaceable:

H2CO3+Na+→NaHCO3+H+

Only one hydrogen atom is released; the other remains bound. In 1 mole of carbonic acid, there is only 1 mole of replaceable hydrogen. The gEq of carbonic acid is the same as its gram formula weight, or 61 g.

Gram Equivalent Weight of a Base

The equivalent weight of a base is its weight (grams) containing 1 mole of replaceable hydroxyl (OH⁻) ions. Similar to acids, the gEq of bases is calculated by dividing gram formula weight by the number of OH⁻ groups in its formula.

Conversion of Gram Weight to Equivalent Weight

To determine the number of gEqs in a substance, the gram weight is divided by its calculated equivalent weight, as shown in the following example:

58.5g NaClgEq58.5g=1gEq

29.25g NaClgEq58.5=0.5gEq

Milligram Equivalent Weights

The concentrations of most chemicals in the body are quite small. The term milligram equivalent weight (milliequivalent) is preferred for expressing these minute values; 1 mEq is simply 0.001 gEq:

mEq=gEq1000

The normal concentration of potassium (K⁺) in plasma ranges from 0.0035 to 0.005 gEq/L. These values may be converted to milliequivalents by multiplying by a factor of 1000. The normal concentration of K⁺ in the plasma would be expressed as ranging from 3.5 to 5.0 mEq/L.

Solute Content by Weight

The measurement of many electrolytes is based on actual weight rather than on milliequivalents. This weight is often expressed as milligrams per 100 ml of blood or body fluid. The units for this measurement are abbreviated as mg% (mg percent) or mg/dl (milligrams per deciliter). This text uses the modern designation mg/dl. Some substances present in blood or body fluid are present in extremely small amounts and are expressed in micrograms ( of a milligram) per deciliter (µg/dl or mcg/dl).

Values stated in mg/dl may be converted into their corresponding equivalent weights and reported as mEq/L. Conversion between mEq/L and mg/dl may be calculated as follows:

mEq/L=mg/dl×10Equivalent weight (1)

(1)

mEq/L=mEq/L×Equivalent weight10 (2)

(2)

To convert a serum Na⁺ value of 322 mg/dl to mEq/L, the equation is used as follows:

mEq/L=mg/dl×10Equivalent weight=322×1023=140 mEq/L

In clinical practice, electrolyte replacement is common when a laboratory test identifies a significant deficiency. The electrolyte content of intravenous solutions is usually stated in milligrams per deciliter or in mEq per liter. Lactated Ringer’s solution is one such infusion used for electrolyte replacement (Table 12-2).

Calculating Solute Content

In addition to gEq, mEq, mg/dl, and µg/dl (mcg/dl), several other methods of calculating solute content exist. These common chemical standards are used to compute solute content and dilution of solutions.

Quantitative Classification of Solutions

The amount of solute in a solution may be quantified by the following six methods:

1. Ratio solution. The amount of solute to solvent is expressed as a proportion (e.g., 1 : 100). Ratio solutions are sometimes used in describing concentrations of drugs.

2. Weight-per-volume solution (W/V). The W/V solution is commonly used for solids dissolved in liquids. It is defined as weight of solute per volume of solution. This method is sometimes erroneously described as a percent solution. W/V solutions are commonly expressed in grams of solute per 100 ml of solution. For example, 5 g of glucose dissolved in 100 ml of solution is properly called a 5% solution, according to the W/V scheme. A liquid dissolved in a liquid is measured as volumes of solute to volumes of solution.

3. Percent solution. A percent solution is weight of solute per weight of solution. For example, 5 g of glucose dissolved in 95 g of water is a true percent solution. The glucose is 5% of the total solution weight of 100 g.

4. Molal solution. A molal solution contains 1 mole of solute per kilogram of solvent, or 1 mmol/g solvent. The concentration of a molal solution is independent of temperature.

5. Molar solution. A molar solution has 1 mole of solute per liter of solution, or 1 mmol/ml of solution. Solute is measured into a container, and solvent is added to produce the solution volume desired.

6. Normal solution. A normal solution

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