Problem 17 - Chemical Principles: The Quest for Insight

Question

What mass (in grams) of anhydrous sohute is needed to prepare each of the following solutions? (a) \(1.0 \mathrm{~L}\) of \(0.10 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}) ;\) (b) \(250 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) \(\mathrm{CaCl}_{2}(\mathrm{aq}) ;\) (c) \(500 \mathrm{~mL}\) of \(0.63 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})\).

Step-by-Step Solution

Answer

For (a) approximately 5.844 grams of NaCl are needed, for (b) approximately 2.775 grams of CaCl2 are needed, and for (c) approximately 56.780 grams of C6H12O6 are needed.

Step 1 - Calculate mass of NaCl for solution (a)

First find the molar mass of NaCl which is the sum of the atomic masses of sodium (Na, approximately 22.99 g/mol) and chlorine (Cl, approximately 35.45 g/mol). The molar mass of NaCl is thus approximately 58.44 g/mol. Next, use the formula mass = molarity (M) * volume (L) * molar mass (g/mol). For a 0.10 M NaCl solution, mass = 0.10 mol/L * 1.0 L * 58.44 g/mol.

Step 2 - Calculate mass of CaCl2 for solution (b)

Identify the molar mass of CaCl2 which is the sum of the atomic masses of calcium (Ca, approximately 40.08 g/mol) and chlorine (Cl, two atoms, approximately 35.45 g/mol each). The molar mass of CaCl2 is thus approximately 110.98 g/mol. Use the formula mass = molarity (M) * volume (L) * molar mass (g/mol). Since the volume is given in milliliters, convert it to liters by dividing by 1000. For 250 mL of 0.10 M CaCl2 solution, the volume in liters is 0.250 L, so mass = 0.10 mol/L * 0.250 L * 110.98 g/mol.

Step 3 - Calculate mass of C6H12O6 for solution (c)

Calculate the molar mass of C6H12O6 by summing up the atomic masses: carbon (C, 6 atoms, approximately 12.01 g/mol each), hydrogen (H, 12 atoms, approximately 1.008 g/mol each), and oxygen (O, 6 atoms, approximately 16.00 g/mol each). The molar mass of glucose is approximately 180.16 g/mol. Use the mass calculation formula with the volume converted to liters (500 mL is equal to 0.500 L): mass = 0.63 mol/L * 0.500 L * 180.16 g/mol.

Key Concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's essentially the recipe for a chemical reaction, telling us how much of each substance is involved. To solve stoichiometric problems, you need to understand the mole concept, balance chemical equations, and use the coefficients from the balanced equation to develop mole-mole conversion factors.

When preparing chemical solutions, stoichiometry allows us to calculate the exact amount of substance (solute) required to achieve a desired concentration in a certain volume of solvent. This is critical in fields such as chemistry and biology, where precise chemical concentrations are necessary for reactions to occur as expected.

Mole Concept

The mole is a fundamental concept in chemistry that acts as a bridge between the microscopic world of atoms and the macroscopic world we can measure. One mole is defined as the number of atoms in exactly 12 grams of carbon-12, which is approximately 6.022 x 10²³ atoms, known as Avogadro's number.

The mole concept allows us to count particles by weighing them. Molar mass, the mass of one mole of a substance in grams, plays a crucial role in stoichiometry because it helps convert between mass and moles. This makes it possible to calculate how many moles of a substance are present in a given mass, a key step in stoichiometric calculations and essential for preparing solutions of desired molarity.

Chemical Solution Preparation

Preparing a chemical solution involves dissolving a specified amount of solute (the substance being dissolved) into a solvent (the substance doing the dissolving) to create a homogenous mixture. The steps involve calculating the required amount of solute, measuring that amount accurately, and then dissolving it into the appropriate volume of solvent.

In a laboratory setting, precision is crucial for reproducibility and accuracy of results. The use of molar mass in these calculations ensures that the correct number of moles is present in the solution. For students and chemists, understanding how to prepare solutions with specific molarities is vital, as it affects the outcome of chemical reactions and experiments.

Molarity

Molarity is a measure of concentration used in chemistry to indicate the number of moles of solute per liter of solution (mol/L). It's a convenient way to express concentration because it allows chemists to easily communicate how much solute is present in a given volume of solution, which is essential for reactions to proceed correctly.

When you're asked to prepare a solution of a certain molarity, you use the formula molarity (M) = moles of solute / volume of solution in liters (L). This is highlighted in the problem by calculating the mass of solute needed to achieve the desired molar concentration in a specific volume of solvent. One common student challenge is remembering to convert milliliters to liters, as molarity is defined in terms of liters of solution. It's also essential to use the correct molar mass of the solute in calculating the number of moles needed.