Problem 45 - Chemistry The Molecular Science

Question

Calculate the mass in grams of solute needed to prepare each of these solutions. (a) \(250 . \mathrm{mL}\) of \(0.50-\mathrm{M} \mathrm{NaCl}\) (b) \(0.50 \mathrm{~L}\) of 0.15 -M sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) (c) \(200 . \mathrm{mL}\) of \(0.20-\mathrm{M} \mathrm{NaHCO}_{3}\)

Step-by-Step Solution

Answer

(a) 7.305 g NaCl, (b) 25.673 g sucrose, (c) 3.360 g NaHCO₃.

Step 1: Understand Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is given by \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \). For these types of problems, we often need to find the mass of the solute based on a given molarity and volume of solution.

Step 2: Find Moles of Solute (Part a)

Determine the number of moles of sodium chloride (NaCl) required using the formula \( \ ext{moles} = M \times \text{Volume (in L)} \). Given \( M = 0.50 \ ext{ M} \) and \( \ ext{Volume} = 0.250 \ ext{ L} \), the calculation is \( \ ext{moles} = 0.50 \ ext{ M} \times 0.250 \ ext{ L} = 0.125 \ ext{ moles} \).

Step 3: Calculate Mass of NaCl (Part a)

To find the mass, use the formula \( \ ext{mass} = \text{moles} \times \text{molar mass} \). The molar mass of NaCl is approximately 58.44 g/mol. Therefore, \( \ ext{mass} = 0.125 \ ext{ moles} \times 58.44 \ ext{ g/mol} = 7.305 \ ext{ grams} \).

Step 4: Find Moles of Solute (Part b)

For sucrose (\( \ ext{C}_{12} \ ext{H}_{22} \ ext{O}_{11} \)), use the formula \( \ ext{moles} = M \times \ ext{Volume (in L)} \). Given \( M = 0.15 \ ext{ M} \) and \( \ ext{Volume} = 0.50 \ ext{ L} \), the calculation is \( \ ext{moles} = 0.15 \ ext{ M} \times 0.50 \ ext{ L} = 0.075 \ ext{ moles} \).

Step 5: Calculate Mass of Sucrose (Part b)

The molar mass of sucrose (\( \ ext{C}_{12} \ ext{H}_{22} \ ext{O}_{11} \)) is approximately 342.30 g/mol. Therefore, \( \ ext{mass} = 0.075 \ ext{ moles} \times 342.30 \ ext{ g/mol} = 25.6725 \ ext{ grams} \).

Step 6: Find Moles of Solute (Part c)

Determine the number of moles of sodium bicarbonate (\( \ ext{NaHCO}_{3} \)) using the formula \( \ ext{moles} = M \times \ ext{Volume (in L)} \). Given \( M = 0.20 \ ext{ M} \) and \( \ ext{Volume} = 0.200 \ ext{ L} \), the calculation is \( \ ext{moles} = 0.20 \ ext{ M} \times 0.200 \ ext{ L} = 0.040 \ ext{ moles} \).

Step 7: Calculate Mass of NaHCO3 (Part c)

The molar mass of \( \ ext{NaHCO}_{3} \) is approximately 84.01 g/mol. Therefore, \( \ ext{mass} = 0.040 \ ext{ moles} \times 84.01 \ ext{ g/mol} = 3.3604 \ ext{ grams} \).

Key Concepts

Moles of Solute

Moles of solute is an essential concept in chemistry, especially when dealing with solutions. It refers to the amount of solute, a substance dissolved in a solvent, in a chemical solution. The mole is a fundamental unit in chemistry that quantifies the amount of substance.

• It typically represents Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles per mole.
• To calculate the moles of solute, you can use the formula:
  \(\text{Moles of Solute} = \text{Molarity (M)} \times \text{Volume (L)}\).

This formula is crucial for finding how many moles are present in a given solution. Knowing this helps in further calculations such as finding the mass of the solute.

Mass of Solute

The mass of solute is another critical measurement in preparing solutions. This refers to the actual weight, in grams, of the solute that is dissolved in the solution.

• The mass can be found once you know the number of moles of solute present in the solution.
• To calculate the mass of the solute, use the equation:
  \(\text{Mass (g)} = \text{Moles of Solute} \times \text{Molar Mass (g/mol)}\).

This mathematical operation allows you to convert moles into grams, providing a more tangible way of understanding how much of a substance is present in a solution. Accurately weighing the solute is vital for creating solutions with specific concentrations.

Molar Mass

Molar mass is an important concept in chemistry that provides the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol).

• To compute the molar mass, sum the atomic masses of all atoms in a molecule. These values can be found on the periodic table.
• For example, for sodium chloride (NaCl), the molar mass is calculated by adding the atomic masses of \(\text{Na}=23\, \text{g/mol}\) and \(\text{Cl}=35.44\, \text{g/mol}\), totaling \(58.44\, \text{g/mol}\).

Having this value helps translate moles into grams, assisting in determining the precise quantity of a substance needed for a particular solution concentration.

Solution Concentration

Solution concentration tells us how much of a solute is present in a given quantity of solvent or solution. Molarity is the most common unit for expressing concentration in chemistry.

• Molarity (M) is defined as \(\frac{\text{moles of solute}}{\text{liters of solution}}\).
• This measurement offers a convenient way to express the concentration and prepare specific solution strengths for experiments.
• High molarity means more solute per volume unit, while low molarity means less solute.

Understanding solution concentration is pivotal in both quantitative and analytical chemistry, ensuring reactions proceed with the proper proportion of reactants.