Glucose is a monosaccharide with a molecular weight of 180 (the sum of its atomic weights). Sucrose is a disaccharide of glucose and fructose, which have molecular weights of 180 each. When glucose and fructose join together by dehydration synthesis to form sucrose, a molecule of water (molecular weight = 18) is split off. Therefore, sucrose has a molecular weight of 342 (180 + 180 - 18). Since the molecular weights of sucrose and glucose are in a ratio of 342/180, it follows that 342 grams of sucrose must contain the same number of molecules as 180 grams of glucose.
Notice that an amount of any compound equal to its molecular weight in grams must contain the same number of molecules as an amount of any other compound equal to its molecular weight in grams. This unit of weight, a mole, always contains 6.02 x 1023 molecules (Avogadro's number). One mole of solute dissolved in water to make one liter of solution is described as a one-molar solution (abbreviated 1.0 M). Although this unit of measurement is commonly used in chemistry, it is not completely desirable in discussions of osmosis because the exact ratio of solute to water is not specified. For example, more water is needed to make a 1.0 M NaCl solution (where a mole of NaCl weighs 58.5 grams) than is needed to make a 1.0 M glucose solution, since 180 grams of glucose takes up more volume than 58.5 grams of salt.
Since the ratio of solute to water molecules is of critical importance in osmosis, a more desirable measurement of concentration is molality. In a one-molal solution (abbreviated
132 Chapter Six
132 Chapter Six
Volume = Z
■ Figure 6.9 The osmolality of a solution. The osmolality (Osm) is equal to the sum of the molalities of each solute in the solution, If a selectively permeable membrane separates two solutions with equal osmolalities, no osmosis will occur,
1.0 m), 1 mole of solute (180 grams of glucose, for example) is dissolved in 1 kilogram of water (equal to 1 liter at 4° C). A 1.0 m NaCl solution and a 1.0 m glucose solution therefore both contain a mole of solute dissolved in exactly the same amount of water (fig. 6.8).
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