Question

Calculate the number of grams of each solute that has to be taken to make each of the following solutions. (a) \(125 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{NaCl}\) (b) \(250.0 \mathrm{~mL}\) of \(0.360 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (c) \(250.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\)

Short answer

To prepare the solutions: (a) 1.46 grams of NaCl, (b) 18.02 grams of C6H12O6, and (c) 6.13 grams of H2SO4 are required.

Step-by-step solution

- Calculate the number of moles of NaCl for solution (a)

First, calculate the moles of NaCl required using the molarity equation, where Molarity (M) = moles of solute / liters of solution. For 0.200 M NaCl and a volume of 125 mL (which is 0.125 L), the moles of NaCl are calculated as: Moles of NaCl = molarity × volume = 0.200 M × 0.125 L.

- Convert moles of NaCl to grams for solution (a)

Using the molar mass of NaCl (approximately 58.44 g/mol), the mass in grams is calculated by: Mass of NaCl = moles of NaCl × molar mass of NaCl = moles of NaCl × 58.44 g/mol.

- Calculate the number of moles of C6H12O6 for solution (b)

Repeat the same process for C6H12O6. Calculate the moles of C6H12O6 needed using the molarity and volume: Moles of C6H12O6 = 0.360 M × 0.250 L.

- Convert moles of C6H12O6 to grams for solution (b)

Find the molar mass of C6H12O6 (approximately 180.16 g/mol), and calculate the mass in grams: Mass of C6H12O6 = moles of C6H12O6 × molar mass of C6H12O6.

- Calculate the number of moles of H2SO4 for solution (c)

Calculate the moles of H2SO4 using its molarity and the given volume: Moles of H2SO4 = 0.250 M × 0.250 L.

- Convert moles of H2SO4 to grams for solution (c)

Using the molar mass of H2SO4 (approximately 98.08 g/mol), calculate the mass of H2SO4 needed: Mass of H2SO4 = moles of H2SO4 × molar mass of H2SO4.

Key concepts

Molar Mass

The molar mass of a substance is the weight in grams of one mole of that substance. It is an essential concept in chemistry as it connects the microscopic world of atoms and molecules to the macroscopic world of grams and liters. The molar mass is numerically equal to the atomic or molecular mass of the substance in atomic mass units (amu).

For example, NaCl (sodium chloride) has a molar mass of 58.44 grams per mole, meaning one mole of NaCl, which contains Avogadro's number of molecules (approximately 6.022 \( \times \) 10\(^{23}\)), weighs 58.44 grams.

Understanding how to find and use the molar mass is fundamental when calculating the number of grams needed in a solution preparation. It is also crucial when converting between moles and grams, since the molar mass serves as the conversion factor in such calculations.

Moles to Grams Conversion

Conversion between moles and grams is a common task in chemistry that relies on the molar mass of a compound. The conversion process is a simple multiplication or division, depending on the direction of the conversion. To convert moles to grams, you multiply the number of moles by the molar mass of the substance. Inversely, to convert grams to moles, you divide the mass of the substance by its molar mass.

This step is crucial when determining how much of a chemical substance is needed to prepare a solution with a specific concentration. For instance, if you need to prepare a 0.200 M solution of NaCl and you've calculated that you need 0.025 moles of NaCl, you would multiply 0.025 moles by the molar mass of NaCl (58.44 g/mol) to determine the mass in grams necessary for your solution.

Solution Preparation

Solution preparation involves dissolving a specified amount of solute in a solvent to reach a desired concentration and volume of solution. Molarity, the measure of concentration, is denoted in moles per liter (M). When preparing a solution, you first determine the desired molarity and the volume of solution you want to prepare.

Following the calculation of the needed moles of solute using the formula:
\[ \text{Moles of solute} = \text{Molarity} (M) \times \text{Volume of solution in liters} (L) \]
you then convert those moles to grams using the moles to grams conversion as described previously. You weigh out the appropriate amount of solute and dissolve it in a solvent, often water, to reach the desired final volume. For example, to prepare 250.0 mL of a 0.250 M H₂SO₄ solution, you'll first calculate the number of moles of H₂SO₄ required and then measure out the corresponding mass based on its molar mass. This process must be done carefully to ensure accuracy and precision in the solution preparation.