Question

Write a detailed set of instructions for making two solutions: (1) \(100 \mathrm{~mL}\) of \(12 \mathrm{M}\) NaOH from solid sodium hydroxide and (2) \(1.00 \mathrm{~L}\) of \(0.1 \mathrm{M} \mathrm{NaOH}\) from your first solution. You have in your lab: volumetric flasks marked to contain \(100.0 \mathrm{~mL}\) and \(1.000 \mathrm{~L},\) a graduated cylinder, and a balance.

Short answer

To prepare the 12 M solution, dissolve 48 g of NaOH in enough water to make 100 mL. From this, use 8.33 mL to prepare 1 L of 0.1 M NaOH solution by diluting with water to the mark.

Step-by-step solution

Calculate the Mass of NaOH for the Concentrated Solution

To prepare 100 mL of a 12 M NaOH solution, calculate the mass of solid NaOH needed using the molarity formula, M = moles/L. Rearrange to moles = M × L. Convert 100 mL to L by dividing by 1000, thus: 100 mL / 1000 = 0.1 L. The molar mass of NaOH is approximately 40 g/mol. Moles of NaOH = 12 M × 0.1 L = 1.2 moles. Mass of NaOH = moles × molar mass = 1.2 mol × 40 g/mol = 48 grams.

Dissolve the NaOH to Prepare the Concentrated Solution

Carefully weigh out 48 grams of solid NaOH using the balance. Gradually add the solid NaOH to the 100 mL volumetric flask containing some distilled water. STIR gently until the NaOH dissolves completely. Once dissolved, add distilled water to the flask until the bottom of the meniscus is at the 100 mL mark of the flask. Use a wash bottle or pipette for accuracy. Mix the solution by inverting the sealed flask several times.

Calculate the Volume of Concentrated Solution for the Dilute Solution

Use the dilution formula M1V1 = M2V2, where M1 and V1 are the molarity and volume of the concentrated solution, and M2 and V2 are the molarity and volume of the diluted solution. Plugging in the values, 12 M × V1 = 0.1 M × 1.00 L. Solve for V1 to find the volume of concentrated solution needed to make the dilute solution. V1 = (0.1 M × 1.00 L) / 12 M = 0.00833 L or 8.33 mL.

Prepare the Dilute NaOH Solution

Use a graduated cylinder to measure 8.33 mL of the concentrated NaOH solution. Carefully transfer this volume to the 1.000 L volumetric flask. Then add distilled water to the flask until the bottom of the meniscus is at the 1.000 L mark. As before, mix the solution well by inverting the sealed flask multiple times.

Key concepts

Solution Preparation

To kick off your laboratory work efficiently, it's vital to understand how to prepare chemical solutions correctly. The term 'chemical solution' can refer to a mixture where one substance, called the solute, is dissolved in another, known as the solvent.

Preparing a chemical solution requires accuracy and safety. For a solid solute like sodium hydroxide (NaOH), you start by calculating the quantity needed for the desired solution concentration. After donning your safety equipment, you would weigh the solid NaOH and slowly add it to a portion of the solvent in a container — commonly, we use distilled water as a solvent.

It's crucial to add solute to solvent, not the other way round, to avoid splashes or exothermic reactions, which can occur with NaOH and water. Once the NaOH is added, stir gently until fully dissolved. While doing so, be aware of the heat generated by the process. After the solute is completely dissolved, add more solvent until you reach the desired final volume, using the accurate calibration mark on your volumetric flask. This attention to detail ensures the intended molarity of your solution is achieved.

Molarity Calculation

Understanding molarity is crucial for anyone hoping to work in chemistry. Molarity, denoted as M, is a way of expressing the concentration of a solution. It's defined as the number of moles of a solute per liter of solution (mol/L).

To calculate the molarity of a NaOH solution, you would use the formula:
\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
The problem requires you to prepare a 12 M solution, which means each liter of solution contains 12 moles of NaOH. To find the amount needed, you convert the volume from milliliters to liters and then multiply this volume by the molarity to find the moles required. With NaOH's molar mass, you can then convert these moles to grams, the practical measure you would use to weigh out the solid compound.

For instance, if you need a 0.1 M solution, you would work backward from the desired molarity and volume to ascertain the volume of the more concentrated stock solution required. This systematic approach to molarity ensures precision and is fundamental in preparative chemistry.

Dilution of Solutions

Diluting a solution is essential when the solution you require is less concentrated than what you have on hand. The dilution process typically involves adding more solvent while keeping the amount of solute constant.

This technique is grounded in the principle that the total amount of solute remains unchanged before and after dilution. Hence, the concentration of the solute decreases as the volume of the solution is increased. The formula encapsulating this relationship is:
\[ M_1V_1 = M_2V_2 \]
where

• \( M_1 \) is the molarity of the initial concentrated solution,


• \( V_1 \) is the volume of the concentrated solution required,


• \( M_2 \) is the molarity of the final diluted solution, and


• \( V_2 \) is the volume of the final diluted solution.

Using this formula, you can determine the exact volume of the concentrated solution you need to achieve a new target concentration after dilution. Remember to mix the final solution thoroughly to ensure that the solute is uniformly distributed throughout the solvent. Dilution is not only practical for preparing less concentrated solutions from more concentrated ones but also critical for tailoring solutions to the appropriate concentration for a variety of experimental or industrial processes.