Question

Sodium hydroxide solutions of different concentrations are needed routinely in most chemistry laboratories. Calculate the masses of NaOH required to prepare 1.00 L each of \(0.100,0.500,3.00,\) and \(6.00 M\) solutions.

Short answer

To prepare 1.00 L of each solution, the required masses of NaOH are: 4.00 g for the 0.100 M solution, 20.00 g for the 0.500 M solution, 120.00 g for the 3.00 M solution, and 240.00 g for the 6.00 M solution.

Step-by-step solution

Identify the given values

We are given the following values for each solution: 1. Molarity (M) = 0.100 M 2. Molarity (M) = 0.500 M 3. Molarity (M) = 3.00 M 4. Molarity (M) = 6.00 M Volume of each solution = 1.00 L

Calculate moles of NaOH

For each solution, use the formula Molarity = moles of solute / liters of solution to calculate the moles of NaOH required: 1. 0.100 M = moles / 1.00 L → moles = 0.100 mol 2. 0.500 M = moles / 1.00 L → moles = 0.500 mol 3. 3.00 M = moles / 1.00 L → moles = 3.00 mol 4. 6.00 M = moles / 1.00 L → moles = 6.00 mol

Calculate the molar mass of NaOH

The molar mass of NaOH can be calculated by summing the molar masses of its elements: Na (22.99 g/mol), O (16.00 g/mol), and H (1.01 g/mol). Molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol

Convert moles of NaOH to mass

Finally, convert the moles of NaOH to mass for each solution using the molar mass of NaOH (40.00 g/mol): 1. Mass = 0.100 mol * 40.00 g/mol = 4.00 g 2. Mass = 0.500 mol * 40.00 g/mol = 20.00 g 3. Mass = 3.00 mol * 40.00 g/mol = 120.00 g 4. Mass = 6.00 mol * 40.00 g/mol = 240.00 g

Summarize the results

The masses of NaOH required to prepare 1.00 L of each concentration are as follows: 1. 0.100 M solution: 4.00 g of NaOH 2. 0.500 M solution: 20.00 g of NaOH 3. 3.00 M solution: 120.00 g of NaOH 4. 6.00 M solution: 240.00 g of NaOH

Key concepts

Solution Preparation

When preparing a solution, especially in a laboratory setting, accuracy is key. The process involves dissolving a specific amount of solute, in this case, sodium hydroxide (NaOH), into a solvent—typically water—to achieve the desired concentration. Here's a simple way to understand the preparation:

• Choose the concentration you need, which in this problem ranges from 0.100 M to 6.00 M.
• Determine the volume of solution desired, which is 1 L in this case.
• Calculate the exact mass of solute needed using its molar mass and the solution's molarity.

To achieve precise results, use a balance to weigh the NaOH and a volumetric flask to ensure the solution volume is accurate. Mix the solute thoroughly with the solvent until it is fully dissolved, ensuring an undisturbed mixture throughout the mixture.

Molar Mass

Molar mass is an essential concept in chemistry, particularly when calculating material quantities for reactions and solutions. It represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). For sodium hydroxide (NaOH), its molar mass combines the atomic masses of its constituent elements:

• Sodium (Na): 22.99 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol

Adding these: 22.99 + 16.00 + 1.01 gives a molar mass of 40.00 g/mol for NaOH. Knowing the molar mass is vital because it allows us to convert between moles and grams—key for solution preparation. Always remember, the molar mass is the foundation for these calculations and ensures you can accurately measure and mix the proper quantities.

Concentration Calculations

Concentration is a term used to describe the amount of a solute dissolved in a solvent. In this problem, molarity (M), defined as moles of solute per liter of solution, is the concentration unit.The formula to calculate moles of solute is:\[\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}\]This equation can be rearranged to:\[\text{moles of solute} = \text{Molarity} \times \text{liters of solution}\]By determining the moles needed, you can then use the molar mass to find the mass of solute required. In the exercise example:

• 1 L of 0.100 M NaOH requires 0.100 mol of NaOH.
• The mass of NaOH needed: 0.100 mol \times 40.00 g/mol = 4.00 g.

Repeat these calculations for each concentration to find the mass required. This method allows you to carefully calculate how much solute you need to prepare a precise solution every time.