Question

If \(125 \mathrm{g}\) of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), is dissolved in enough water to make \(450 .\) mL of solution, calculate the molarity.

Short answer

The molarity of the sucrose solution is approximately \(0.81 \, \text{mol/L}\).

Step-by-step solution

Calculate the molar mass of sucrose

To calculate the molar mass of sucrose (C12H22O11), add the molar masses of each of its constituent elements: Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of sucrose = 12 × 12.01 + 22 × 1.01 + 11 × 16.00 = 144.12 + 22.22 + 176.00 = 342.34 g/mol

Calculate the number of moles of sucrose in 125 g

Now, we can find the number of moles of sucrose using the given mass of sucrose (125 g) and its molar mass (342.34 g/mol): Number of moles = mass / molar mass = 125 g / 342.34 g/mol = 0.365 mol

Convert the volume of the solution from mL to L

The given volume of the solution is 450 mL. We need to convert it to liters: 1 L = 1000 mL So, 450 mL = 450/1000 L = 0.45 L

Calculate the molarity of the sucrose solution

Finally, we can find the molarity by dividing the number of moles of sucrose by the volume of the solution in liters: Molarity = moles / volume = 0.365 mol / 0.45 L = 0.81 mol/L The molarity of the sucrose solution is approximately 0.81 mol/L.

Key concepts

Molar Mass of Sucrose

Understanding the molar mass of a substance is essential for many chemistry calculations, including molarity. The molar mass represents the weight of one mole of a substance and is expressed in grams per mole (g/mol). In the case of sucrose, a disaccharide composed of glucose and fructose, it has the molecular formula \textbf{C}\(_{12}\)\textbf{H}\(_{22}\)\textbf{O}\(_{11}\).

To calculate the molar mass of sucrose, you sum the molar masses of each of its constituent atoms: carbon (C), hydrogen (H), and oxygen (O). Considering their respective weights—carbon at 12.01 g/mol, hydrogen at 1.01 g/mol, and oxygen at 16.00 g/mol—you end up with a molar mass of 342.34 g/mol. This step in the solution is pivotal because the molarity calculation later relies on the number of moles, which we derive using this molar mass.

Keep in mind that the molar masses of the elements are constants and can be found in a periodic table, enabling consistency across various chemical calculations.

Moles Calculation

The concept of moles is fundamental in chemistry and is used to relate masses of substances to the number of particles they contain. One mole corresponds to Avogadro's number, which is approximately 6.022 × 10\(^{23}\) particles. In the context of our problem, we're asked to find the number of moles in a specific quantity of sucrose.

To perform this moles calculation, divide the given mass of the substance (125 g of sucrose in this case) by its molar mass (342.34 g/mol). The solution shows this calculation: 125 g / 342.34 g/mol = 0.365 mol. This gives the number of moles of sucrose present in our sample, which is the basis for determining the solution's concentration in the final step. Remember, the accuracy of this calculation affects the accuracy of the molarity, so it's crucial to calculate the number of moles correctly.

Solution Concentration

Solution concentration is a measure of how much solute is dissolved in a given volume of solvent. Molarity is one of the most commonly used units to express concentration, indicating moles of solute per liter of solution (mol/L).

In our exercise, to find the molarity, we divide the amount of moles of sucrose (0.365 mol) by the volume of the solution in liters (0.45 L). The calculation proceeds as 0.365 mol / 0.45 L, yielding a molarity of 0.81 mol/L. This value tells us that every liter of the sucrose solution contains 0.81 moles of sucrose.

Understanding how to calculate solution concentration is important not only for laboratory work but also in industrial applications where precise concentrations are crucial for desired outcomes. Solution concentration can also affect properties like boiling point, freezing point, and osmotic pressure, linking it to a wide array of scientific studies and applications.