Question

The molecular mass of glucose is about \(180 \mathrm{g} / \mathrm{mol}\). If \(45 \mathrm{g}\) of glucose is dissolved in water to make a final volume of \(0.5 \mathrm{L},\) what is the molarity of the solution? a. \(0.125 \mathrm{M}\) b. \(0.25 \mathrm{M}\) c. \(0.5 \mathrm{M}\) d. \(1.0 \mathrm{M}\) e. \(2.0 \mathrm{M}\)

Short answer

The molarity of the solution is \(0.5 M\), so option c is correct.

Step-by-step solution

Calculate the number of moles of glucose

The number of moles can be calculated by dividing the mass of the substance by its molecular mass. The mass of glucose given is 45g and its molecular mass is 180g/mol. So number of moles of glucose = \(\frac{45g}{180g/mol} = 0.25 mol\)

Calculate the volume of the solution in liters

The volume of the solution is given as 0.5L. So we do not need to do any conversions.

Calculate the molarity

Now, we calculate the molarity of the solution by dividing the number of moles of solute by the volume of the solution in liters. Molarity = \(\frac{Number of moles of solute}{Volume of solution in liters} = \frac{0.25 mol}{0.5 L} = 0.5 M\)

Key concepts

Moles

The concept of 'moles' is a fundamental aspect of chemistry, crucial for understanding the quantity of a substance involved in chemical reactions.

Moles provide a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms. When we talk about moles, we're referring to a specific number of particles, atoms, or molecules. This number is called Avogadro's number, and it is approximately equal to \(6.022 \times 10^{23}\) particles per mole.

To calculate moles when given the mass of a substance, you divide the mass by the molar mass of the substance. The unit for measuring moles is simply 'mol'. This calculation was essential in the textbook exercise to determine the amount of glucose in moles before proceeding to calculate the molarity of the solution.

Solution Concentration

Solution concentration describes how much of a solute is present in a given quantity of solvent. Understanding concentration is key to fields like chemistry, biology, and medicine, where precise measurements are necessary.

One common unit of concentration is molarity, expressed as moles of solute per liter of solution (mol/L). Molarity provides insight into the strength of the solution and its potential reactivity. In our textbook exercise, after calculating the moles of glucose, the next step was to find out the molarity by dividing these moles by the volume of the solution. This step is crucial for determining the solution’s concentration.

Molar Mass

Molar mass is the mass of one mole of a substance and its units are grams per mole (g/mol). It can be found on the periodic table for elements and calculated for compounds by adding up the molar masses of the individual elements.

The molar mass allows chemists to convert between mass of a substance and moles, which is helpful for creating solutions with precise concentrations. In the exercise, molar mass was used to calculate the number of moles of glucose from the given mass. Knowing the molar mass of glucose (180 g/mol), we can see how crucial it is for conducting accurate molarity calculations.