Question

When a diabetic experiences low blood glucose, possibly due to an excess of insulin or increased levels of exercise, the treatment is consumption of glucose tablets. (a) How many grams of glucose are in the recommended amount for treatment of an adult, \(0.0833\) mol glucose? (b) A typical tablet contains \(3.75 \mathrm{~g}\) of glucose. How many tablets should be eaten? (c) How many molecules of glucose are in \(0.0833\) mol?

Short answer

(a) 15.01 g, (b) 4 tablets, (c) \(5.02 \times 10^{22}\) molecules.

Step-by-step solution

Convert Moles to Grams for Part (a)

To find the mass of glucose in grams from moles, use the formula:\[\text{mass (g)} = \text{moles} \times \text{molar mass} \]The molar mass of glucose (\(C_6H_{12}O_6\)) is calculated as follows:- Carbon (C): \(12.01 \times 6 = 72.06\)- Hydrogen (H): \(1.01 \times 12 = 12.12\)- Oxygen (O): \(16.00 \times 6 = 96.00\)Add them: \(72.06 + 12.12 + 96.00 = 180.18\, \mathrm{g/mol}\).Now, calculate the mass:\[0.0833 \text{ mol} \times 180.18 \text{ g/mol} = 15.01 \text{ g}\]

Calculate Number of Tablets for Part (b)

Given that each glucose tablet contains \(3.75 \text{ g}\), divide the total grams from Step 1 by this amount:\[\text{Number of tablets} = \frac{15.01 \text{ g}}{3.75 \text{ g/tablet}} \approx 4.00 \text{ tablets}\]Therefore, an adult should consume approximately 4 tablets.

Convert Moles to Molecules for Part (c)

To find the number of molecules from moles, use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol:\[\text{Number of molecules} = 0.0833 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol}\]Perform the multiplication:\[= 5.02 \times 10^{22} \text{ molecules}\]

Key concepts

Molar Mass Calculation

Understanding molar mass is essential in chemistry, especially when dealing with substances like glucose. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It provides a bridge between the atomic scale and the macroscopic scale we observe daily.

For glucose, with the chemical formula \(C_6H_{12}O_6\), the molar mass is derived by summing the atomic masses of each atom within a molecule:

• Carbon (C) has an atomic mass of about 12.01 amu, and there are six carbon atoms: \(12.01 \times 6 = 72.06\)
• Hydrogen (H) has an atomic mass of about 1.01 amu, and there are twelve hydrogen atoms: \(1.01 \times 12 = 12.12\)
• Oxygen (O) has an atomic mass of about 16.00 amu, and there are six oxygen atoms: \(16.00 \times 6 = 96.00\)

Adding these together, the molar mass of glucose is \(72.06 + 12.12 + 96.00 = 180.18\, \mathrm{g/mol}\). This value is crucial when converting between moles and grams of glucose.

Moles to Grams Conversion

Converting moles to grams is a fundamental skill in chemistry. It allows us to translate a given amount (in moles) into a measurable quantity (in grams).

To perform this conversion, we use the formula: \[\text{mass (g)} = \text{moles} \times \text{molar mass}\]In our glucose example, we need to convert 0.0833 moles of glucose to grams. Using the molar mass calculated earlier (\(180.18\, \mathrm{g/mol}\)), we find the mass: \[0.0833 \text{ mol} \times 180.18 \text{ g/mol} = 15.01 \text{ g}\]This tells us that \(0.0833\) moles of glucose corresponds to \(15.01\) grams, which is pertinent for determining the right dosage in glucose tablets.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, essential for converting between moles and individual molecules. It is defined as the number of atoms, ions, or molecules in one mole of a substance, and is approximately \(6.022 \times 10^{23}\).

For our problem, we want to find out how many molecules are in \(0.0833\) moles of glucose. Therefore, the calculation is:

\[\text{Number of molecules} = 0.0833 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol}\]

Performing this multiplication gives us \(5.02 \times 10^{22}\). This immense number shows the vast scale at which molecules exist in even tiny amounts of chemicals, like glucose.

Glucose Tablets

Glucose tablets are a quick and effective way to raise blood sugar levels in individuals experiencing hypoglycemia, particularly persons with diabetes. Each tablet typically contains a specific amount of glucose (usually 3.75 grams per tablet) to allow for controlled and accurate dosing.

In our exercise, after calculating that 0.0833 moles of glucose corresponds to 15.01 grams, we can determine how many tablets are needed by dividing the total grams by the grams per tablet:

• Number of tablets = \(\frac{15.01 \text{ g}}{3.75 \text{ g/tablet}} \approx 4.00 \text{ tablets}\)

This calculation tells us that consuming approximately four tablets would provide the recommended amount of glucose.

Diabetes Treatment

Diabetes management involves careful monitoring and regulation of blood glucose levels. Glucose tablets provide a simple, portable solution for those needing an immediate increase in blood sugar, especially during a hypoglycemic episode.

During hypoglycemia, the prompt intake of glucose tablets helps stabilize blood glucose levels, preventing potential complications associated with low blood sugar.

Understanding the conversions from moles to grams, as well as the number of tablets needed, ensures proper dosing. This knowledge empowers individuals with diabetes to better manage their condition, using scientifically-backed calculations to guide their treatment.