Question

Calculate the grams of solute needed to prepare each of the following solutions: a. \(2.00 \mathrm{~L}\) of a \(1.50 \mathrm{M} \mathrm{NaOH}\) solution b. \(4.00 \mathrm{~L}\) of a \(0.200 \mathrm{M} \mathrm{KCl}\) solution c. \(25.0 \mathrm{~mL}\) of a \(6.00 \mathrm{M} \mathrm{HCl}\) solution

Short answer

Part a: 120 g, Part b: 59.6 g, Part c: 5.475 g

Step-by-step solution

- Understand the formula

The formula to calculate the mass of the solute needed is:\[\text{mass of solute (grams)} = \text{Molarity (M)} \times \text{Volume (L)} \times \text{Molar Mass of solute (g/mol)}\]We will use this formula for each part of the question.

- Calculate for NaOH solution (Part a)

For the NaOH solution:1. Molarity (\text{M}) = 1.50 M2. Volume (\text{V}) = 2.00 L3. Molar Mass of NaOH (Na = 23 g/mol, O = 16 g/mol, H = 1 g/mol) = 40 g/molNow, use the formula:\[\text{Mass of NaOH} = 1.50 \text{ M} \times 2.00 \text{ L} \times 40 \text{ g/mol} = 120 \text{ g}\]

- Calculate for KCl solution (Part b)

For the KCl solution:1. Molarity (\text{M}) = 0.200 M2. Volume (\text{V}) = 4.00 L3. Molar Mass of KCl (K = 39 g/mol, Cl = 35.5 g/mol) = 74.5 g/molNow, use the formula:\[\text{Mass of KCl} = 0.200 \text{ M} \times 4.00 \text{ L} \times 74.5 \text{ g/mol} = 59.6 \text{ g}\]

- Calculate for HCl solution (Part c)

For the HCl solution:1. Molarity (\text{M}) = 6.00 M2. Volume (\text{V}) = 25.0 mL = 0.025 L3. Molar Mass of HCl (H = 1 g/mol, Cl = 35.5 g/mol) = 36.5 g/molNow, use the formula:\[\text{Mass of HCl} = 6.00 \text{ M} \times 0.025 \text{ L} \times 36.5 \text{ g/mol} = 5.475 \text{ g}\]

Key concepts

Molarity

Molarity is a measure of the concentration of a solution. It tells us how many moles of solute are present in one liter of solution. The formula to calculate molarity is:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]
For example, in a 1.50 M NaOH solution, there are 1.50 moles of NaOH per liter of solution. Molarity helps us understand how strong or weak a solution is.

Molar Mass

Molar mass is the mass of one mole of a given substance, expressed in grams per mole (g/mol). To find the molar mass of a compound, we sum the molar masses of its constituent atoms.
For instance, the molar mass of NaOH is calculated by adding the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):
\[ \text{Molar Mass of NaOH} = 23 \text{g/mol (Na)} + 16 \text{g/mol (O)} + 1 \text{g/mol (H)} = 40 \text{g/mol} \]
This value is essential for converting between moles and grams when working with solutions.

Concentration Formulas

To calculate the mass of solute needed for a given solution, we use the formula:
\[ \text{Mass of solute (grams)} = \text{Molarity (M)} \times \text{Volume (L)} \times \text{Molar Mass of solute (g/mol)} \]
This formula allows us to determine the amount of solute in grams required to achieve a specific concentration and volume of solution. Let’s break down the terms:

• Molarity (\text{M}): Concentration in moles per liter
• Volume (\text{V}): Volume of the solution in liters
• Molar Mass: Mass of one mole of the solute in grams

Gram-Mass of Solute

The gram-mass of solute represents the total mass of the solute required to prepare a solution of a certain molarity and volume. Using the given formula, you can determine this mass in grams. For example, to find the mass of NaOH needed to prepare 2.00 L of a 1.50 M NaOH solution:
First, identify the molarity, volume, and molar mass:

• Molarity (M) = 1.50 M
• Volume (V) = 2.00 L
• Molar Mass of NaOH = 40 g/mol

Now, plug these values into the formula:
\[ \text{Mass of NaOH} = 1.50 \text{ M} \times 2.00 \text{ L} \times 40 \text{ g/mol} = 120 \text{ g} \] Therefore, you need 120 grams of NaOH to prepare the solution.

Volume of Solution

The volume of a solution is simply the amount of liquid that contains the solute. It may sometimes need conversion depending on the units provided. For instance, converting milliliters to liters is necessary, as calculations usually use liters.
For example, in the problem involving HCl solution, the volume is given as 25.0 mL, which you need to convert to liters:
\[ 25.0 \text{ mL} = 0.025 \text{ L} \]
This conversion is essential for using the concentration formulas correctly.