Question

An average human being has about \(5.0 \mathrm{~L}\) of blood in his or her body. If an average person were to eat \(32.0 \mathrm{~g}\) of sugar (sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}, 342.30 \mathrm{~g} / \mathrm{mol}\) ), and all that sugar were dissolved into the bloodstream, how would the molarity of the blood sugar change?

Short answer

The change in molarity of blood sugar after an average person consumes 32.0 grams of sugar and it dissolves into their bloodstream would be approximately 0.0187 mol/L.

Step-by-step solution

Converting grams of sugar to moles

First, we need to convert the 32.0 grams of sugar to moles. To do this, we use the molecular weight of sucrose, which is 342.30 g/mol. Moles of sugar = (grams of sugar) / (molecular weight of sucrose) Moles of sugar = \( \frac{32.0~g}{342.30~g/mol} \)

Calculating the molarity of sugar in blood

Now, we'll use the volume of blood in the body and the moles of sugar to find the molarity of sugar in the bloodstream. Molarity = \( \frac{moles~of~sugar}{volume~of~blood~in~liters} \) We know the volume of blood in the body is 5.0 liters. Substituting the values we found in step 1: Molarity = \( \frac{\frac{32.0~g}{342.30~g/mol}}{5.0~L} \)

Simplifying to find the change in molarity of blood sugar

Now, we'll simplify the expression to find the change in molarity of blood sugar. Molarity = \( \frac{32.0~g}{342.30~g/mol \times 5.0~L} \) Molarity ≈ \( \frac{32.0~g}{1711.5~g \cdot L/mol} \) Molarity ≈ \( \frac{32.0}{1711.5} mol/L \) Molarity ≈ 0.0187 mol/L The change in molarity of blood sugar after the sugar is dissolved into the bloodstream would be approximately 0.0187 mol/L.

Key concepts

Conversion of Grams to Moles

One of the fundamental concepts in chemistry is converting grams of a substance into moles. This is essential because chemical reactions are based on moles, not grams. To perform this conversion, you need to know the molecular weight of the substance you'll be converting.

• Molecular weight is expressed in grams per mole (g/mol).
• To find the number of moles of a substance, divide the mass in grams by the molecular weight.

For example, if you have 32 grams of sucrose, which has a molecular weight of 342.30 g/mol, you convert it to moles by using the equation: \(\text{Moles of sucrose} = \frac{32 \, \text{g}}{342.30 \, \text{g/mol}}\).
Rather than thinking in terms of grams, chemists use moles to ensure reactions occur with the correct proportion of substances.

Sucrose

Sucrose is a type of sugar that is commonly found in sweets and desserts. It is a disaccharide composed of glucose and fructose. This sugar is particularly important in both everyday life and biological systems because it serves as a primary energy source.

• Sucrose has the molecular formula \( \text{C}_{12}\text{H}_{22}\text{O}_{11}\).
• Understanding its structure and role can help in fields ranging from nutrition to cellular biology.

When sucrose is consumed, it's broken down by the body into glucose and fructose. These simpler sugars are then absorbed into the bloodstream, where they can be used as energy or stored for later use. Hence, knowing the amount of sucrose in foods is important for dietary considerations, especially for people monitoring their sugar intake due to medical conditions like diabetes.

Molecular Weight

Molecular weight is a critical concept in chemistry used to describe the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and can be calculated by adding up all the atomic weights of the atoms in a molecule. Each element has a standard atomic weight, found on the periodic table, which allows us to perform these calculations. For instance, sucrose (\( \text{C}_{12}\text{H}_{22}\text{O}_{11}\)) has a molecular weight of 342.30 g/mol.
In this case:

• Carbon (C) has an atomic weight of about 12 g/mol. With 12 carbon atoms, that totals 144 g/mol.
• Hydrogen (H) weighs about 1 g/mol. With 22 hydrogen atoms, that's 22 g/mol.
• Oxygen (O) weighs approximately 16 g/mol. With 11 oxygen atoms, that's 176 g/mol.
• By adding these sums, you reach the molecular weight of sucrose, 342.30 g/mol.

Understanding molecular weight allows you to convert between the mass of a substance and the amount in moles, which is fundamental in stoichiometric calculations.

Dissolution in Blood

When substances like sucrose dissolve in blood, they undergo a process where they become evenly distributed in the fluid. Blood, in this case, is the solvent, and sucrose is the solute.
Dissolution is crucial for understanding how substances travel through the body and ultimately affect it. When sucrose enters the bloodstream, it's typically broken down into glucose and fructose, which dissolve easily in the water-based blood plasma. This ensures that these sugars can be delivered to all the cells in the body that require energy.
The process of dissolution affects various bodily functions such as metabolism, and it's essential for maintaining concentration gradients that are vital for cellular function.
By understanding how substances dissolve in blood, scientists and healthcare professionals can better predict the effects and distribution of drugs and nutrients in the body.

Blood Sugar Concentration

Blood sugar concentration refers to the amount of glucose present in the blood at any given time. Having too high or too low levels of blood sugar can lead to health issues, so it's important to maintain these levels within a normal range.

• Normal fasting blood sugar levels for a healthy person typically range from 70 to 99 mg/dL.
• After eating, blood sugar levels usually rise but should not exceed 140 mg/dL in a normal healthy person.

Molarity is a useful measurement when considering how much sugar there is in the blood, as it provides the concentration of the dissolved substance in terms of moles per liter. In the given exercise, we calculated that consuming 32 grams of sucrose could raise blood sugar concentration to approximately 0.0187 mol/L, illustrating how ingested sugars affect overall blood sugar levels. Proper management of blood sugar levels is crucial in preventing conditions such as hypoglycemia and hyperglycemia, which are especially significant for individuals with diabetes. Understanding this helps inform dietary choices and medical treatment plans.