Problem 65 - Chemistry Matter and Change

Question

Complex Carbohydrates Stachyose is a tetrasaccharide that contains two D-galactose units, one D-glucose unit, and one D-fructose unit. Each sugar unit has a molecular weight of 180 g/mol before it is linked together in this tetrasaccharide, and one water molecule is released for each two sugar units that come together. What is the molecular weight of stachyose?

Step-by-Step Solution

Answer

The molecular weight of stachyose can be calculated as follows: first, find the combined molecular weight of all four sugar units by multiplying the molecular weight of each unit (180 g/mol) by the number of units present (720 g/mol). Then, calculate the total molecular weight of the two water molecules released during the formation of stachyose (36 g/mol). Finally, subtract the total molecular weight of the water molecules from the combined molecular weight of all four sugar units to obtain the molecular weight of stachyose: \( 720\,g/mol - 36\,g/mol = 684\,g/mol \).

Step 1: Calculate the combined molecular weight of all four sugar units

To find the combined molecular weight of all four sugar units, we need to multiply the molecular weight of each unit (180 g/mol) by the number of units present: Combined molecular weight of sugar units = 180 g/mol × 4 units = 720 g/mol

Step 2: Calculate the number of water molecules released during the formation of stachyose

As stated in the exercise, one water molecule is released for each two sugar units that come together. Since there are a total of four sugar units, the number of water molecules released during the formation of stachyose is: Number of water molecules released = 4 sugar units / 2 = 2 water molecules

Step 3: Calculate the total molecular weight of the water molecules released

Each water molecule has a molecular weight of 18 g/mol. To find the total molecular weight of the two water molecules released during the formation of stachyose, multiply the molecular weight of one water molecule by the number of water molecules: Total molecular weight of water molecules = 18 g/mol × 2 = 36 g/mol

Step 4: Calculate the molecular weight of stachyose

To find the molecular weight of stachyose, subtract the total molecular weight of the water molecules released from the combined molecular weight of all four sugar units: Molecular weight of stachyose = Combined molecular weight of sugar units - Total molecular weight of water molecules = 720 g/mol - 36 g/mol = 684 g/mol The molecular weight of stachyose is 684 g/mol.

Key Concepts

Carbohydrate Chemistry

Carbohydrate chemistry is a branch of organic chemistry that focuses on the structure, properties, and reactions of carbohydrates. Carbohydrates, also known as saccharides, are essential biomolecules that serve as energy sources and structural components in living organisms. They are classified based on their size and complexity into monosaccharides, disaccharides, oligosaccharides, and polysaccharides.

A tetrasaccharide like stachyose is considered an oligosaccharide because it is composed of between three and ten monosaccharide units. Oligosaccharides are formed through a process called dehydration synthesis, where water molecules are released as the monosaccharides link together via glycosidic bonds. Understanding the molecular structure of carbohydrates like stachyose is integral to calculating their molecular weight, which is important for various biochemical applications including energy calculation and nutritional analysis.

Molecular Formula

The molecular formula of a compound provides information about the exact number and type of atoms present in a molecule. In carbohydrate chemistry, the molecular formula of common monosaccharide units like D-galactose, D-glucose, and D-fructose is typically \( C_6H_{12}O_6 \) before dehydration synthesis. However, during oligosaccharide formation, not all hydrogen and oxygen atoms remain as the molecules condense.

For instance, the linking of two sugar units results in the elimination of a water molecule (H2O), effectively reducing the hydrogen count by two and the oxygen count by one for each glycosidic bond formed. This reduction is critical in determining the molecular weight of the resultant carbohydrate, and an accurate molecular formula is necessary to calculate the molecule's molar mass, or molecular weight.

Stoichiometry

Stoichiometry is a core concept in chemistry that involves the quantitative relationship between reactants and products in a chemical reaction. The stoichiometric calculations are fundamental to understanding chemical processes, such as the formation of oligosaccharides like stachyose.

In this context, stoichiometry is used to calculate the molecular weight of stachyose by considering the number of monosaccharide units and the number of water molecules released during its synthesis. According to the stoichiometry of stachyose formation, one water molecule is released for every two sugar units that bond, requiring us to account for these lost molecules when calculating the overall molecular weight of the oligosaccharide. Hence, a comprehensive grasp of stoichiometric principles is vital for performing accurate molecular weight calculations and for advancing one's knowledge in carbohydrate chemistry.