Problem 16 - Chemistry Matter and Change

Question

What is the molarity of an aqueous solution containing 40.0 \(\mathrm{g}\) of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in \(1,5 \mathrm{L}\) of solution?

Step-by-Step Solution

Answer

The molarity of the solution is approximately 0.148 M.

Step 1: Calculate the molar mass of glucose

The molar mass of glucose (\(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\)) is calculated by adding the molar masses of all atoms in the formula: \[\text{Molar mass of glucose} = (6 \times 12.01) + (12 \times 1.01) + (6 \times 16.00)\]. This results in a molar mass of approximately \(180.18\, \text{g/mol}\).

Step 2: Convert mass of glucose to moles

Using the molar mass, convert 40.0 grams of glucose to moles: \[\text{Moles of glucose} = \frac{40.0\, \text{g}}{180.18\, \text{g/mol}}\]. This results in approximately \(0.222\,\text{mol}\).

Step 3: Calculate molarity

The molarity of the solution is calculated using the formula: \[\text{Molarity} (M) = \frac{\text{moles of solute}}{\text{liters of solution}}\]. Therefore, \(M = \frac{0.222\,\text{mol}}{1.5\, \text{L}}\), which gives a molarity of approximately \(0.148\, M\).

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a compound is essential because it helps us understand the weight of one mole of that compound. For the molecule glucose, with the formula \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\), we need to consider each type of atom the molecule contains. Here's how you can calculate it:

• Carbon has a molar mass of approximately 12.01 g/mol. With 6 carbon atoms in glucose, that's \(6 \times 12.01 = 72.06\,\text{g/mol}\).
• Hydrogen weighs about 1.01 g/mol. Twelve hydrogen atoms contribute \(12 \times 1.01 = 12.12\,\text{g/mol}\).
• Oxygen has a molar mass of 16.00 g/mol, and six oxygen atoms add \(6 \times 16.00 = 96.00\,\text{g/mol}\).

Add them all up: \(72.06 + 12.12 + 96.00 = 180.18\,\text{g/mol}\). By combining each atom's molar mass, we get the molar mass of glucose as approximately 180.18 g/mol.

Conversion Between Grams and Moles

When you have an amount of a substance in grams and want to convert it to moles, you make use of the compound's molar mass. This is a necessary step when calculating molarity.

Using our example with glucose, if you have 40.0 grams, you will apply the conversion formula:

• Take the mass in grams and divide it by the molar mass: \(\frac{\text{mass in grams}}{\text{molar mass}}\).
• For glucose, it's \(\frac{40.0\,\text{g}}{180.18\,\text{g/mol}} = 0.222\,\text{mol}\).

This calculation helps us find how many moles are present in a given mass of glucose, which is crucial for figuring out the solution's molarity.

Glucose Solution

Understanding a glucose solution involves knowing how to compute its molarity, which measures its concentration. Molarity is defined as moles of solute per liter of solution.

• After finding the moles of glucose, you plug the values into the molarity formula: \(M = \frac{\text{moles}}{\text{liters}}\).
• Continuing with our example, \(M = \frac{0.222\,\text{mol}}{1.5\,\text{L}} = 0.148\,\text{M}\).

This value indicates that there are 0.148 moles of glucose in every liter of the solution. Knowing the molarity helps in understanding the solution's concentration, which has practical applications in various scientific and medical fields.