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 molarity of the blood sugar would change by 0.0187 mol/L after the person eats 32.0 g of sugar.

Step-by-step solution

Convert grams of sugar to moles

To convert grams of sugar to moles, we need to use the molar mass given in the exercise \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}, 342.30 \mathrm{g} / \mathrm{mol}\). We have 32.0 g of sugar, so we can use the conversion factor: Moles of sugar = \(\frac{32.0 \,\mathrm{g}}{342.30\, \mathrm{g/mol}}\)

Calculate the volume of blood in liters

Given that an average human being has 5.0 L of blood, we can use this value as the volume in our molarity calculation. Volume of blood = 5.0 L

Calculate the molarity using moles and volume

To find the molarity, we will divide the moles of sugar by the volume of blood in liters. Molarity = \(\frac{\text{moles of sugar}}{\text{Volume of blood in L}}\) Plugging in the values: Molarity = \(\frac{\frac{32.0 \,\mathrm{g}}{342.30\, \mathrm{g/mol}}}{5.0\,\mathrm{L}} = 0.0187\, \mathrm{mol/L}\) Hence, the molarity of the blood sugar would change by 0.0187 mol/L after the person eats 32.0 g of sugar.

Key concepts

Blood Sugar Concentration

Blood sugar concentration refers to the amount of sugar present in the bloodstream. It's usually measured in moles per liter (mol/L) or milligrams per deciliter (mg/dL).
Understanding how sugar concentration changes in the blood is crucial for managing health conditions like diabetes, where blood sugar levels can become a serious concern.
In this context, blood sugar concentration is altered when an external dose of sugar, such as from food intake, dissolves in the bloodstream. Upon consuming sugar, it gets absorbed into the blood and thus increases the overall concentration.
Calculating this concentration helps in determining the precise effect dietary intake of sugar has on your body, which can be vital for dietary planning and health management.

Molecular Weight Calculation

Molecular weight, also known as molar mass, is a crucial factor in converting a substance's mass to its corresponding amount in moles. It is the sum of the atomic weights of all atoms in a molecule.
For the sugar in this exercise, which is sucrose (C\(_{12}\)H\(_{22}\)O\(_{11}\)), the molecular weight is provided as 342.30 g/mol.
This value is obtained by adding up the atomic weights of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms, as per the molecular formula:
\[ \text{Molecular Weight} = (12 \times 12.01) + (22 \times 1.01) + (11 \times 16.00) = 342.30 \, \text{g/mol} \]
By knowing the molar mass of a compound, you can convert grams into moles and vice versa, enabling further calculations involving the substance's quantity in different reactions or solutions.

Moles Conversion

The process of moles conversion involves translating between the mass of a substance and its quantity in moles.
This is necessary since many chemical equations operate in terms of moles rather than grams. This conversion employs the molecular weight as a conversion factor.
In the current scenario, we have 32.0 grams of sucrose, and we need to determine how many moles this represents. The conversion is executed using the formula:
\[ \text{Moles of sugar} = \frac{32.0 \, \text{g}}{342.30 \, \text{g/mol}} \]
This results in approximately 0.0935 moles of sucrose. Understanding moles conversion is fundamental to accurately measuring and predicting the outcomes of chemical reactions in the bloodstream and beyond.