Question

For convenience, one form of sodium hydroxide that is sold commercially is the saturated solution. This solution is \(19.4 M,\) which is approximately \(50 \%\) by mass sodium hydroxide. What volume of this solution would be needed to prepare \(3.50 \mathrm{~L}\) of \(3.00 \mathrm{M} \mathrm{NaOH}\) solution?

Short answer

To prepare \(3.50\,\text{L}\) of \(3.00\,\text{M}\) NaOH solution, \(0.54\,\text{L}\) of the concentrated \(19.4\,\text{M}\) NaOH solution is needed.

Step-by-step solution

Identify known variables

We are given the following information: - Concentrated NaOH solution (C1) = 19.4M - Desired volume of diluted solution (V2) = 3.50 L - Desired concentration of the diluted solution (C2) = 3.00 M Our goal is to find the volume of the concentrated solution needed (V1).

Set up the dilution formula

Using the dilution formula, C1 × V1 = C2 × V2, we have: \(19.4 \,\text{M}\,× V1 = 3.00 \,\text{M}\,× 3.50\,\text{L}\)

Solve for V1

Rearrange the equation to solve for V1: \(V1 = \frac{C2 × V2}{C1}\) Now, substitute the known values for C1, C2, and V2: \(V1 = \frac{3.00\,\text{M}\,× 3.50\,\text{L}}{19.4\,\text{M}}\)

Calculate V1

When we perform the calculation, we get the volume of the concentrated solution that is required: \(V1 = \frac{3.00\,\text{M}\,× 3.50\,\text{L}}{19.4\,\text{M}} = 0.54\,\text{L} \) So, to prepare 3.50 L of 3.00 M NaOH solution, 0.54 L of the concentrated 19.4 M NaOH solution is needed.

Key concepts

Sodium Hydroxide Preparation

Sodium hydroxide (NaOH), also known as lye or caustic soda, is a highly versatile substance used in various industrial processes, such as paper manufacturing, soap making, and water treatment. Preparing a solution of sodium hydroxide in the laboratory or for industrial use requires careful handling due to its corrosive nature. Commercially, it is available in different forms including pellets, flakes, and concentrated aqueous solutions.

Pure sodium hydroxide is actually a solid at room temperature, and when dissolved in water, it releases heat in an exothermic reaction. It is critical to add NaOH to water, rather than pouring water onto NaOH, to control the heat of dissolution and minimize the risk of splashing the caustic solution.

For those who need to prepare a diluted NaOH solution, the process involves measuring a specific volume of a concentrated stock solution and adding water to achieve the desired molarity and volume. To avoid any precipitation or excessive heat, we should always pour NaOH into water slowly, with constant stirring to ensure homogeneity of the resulting solution.

Molarity Concentration

Molarity, symbolized by the capital letter M, is a measure of the concentration of a solution. It represents the number of moles of solute (the substance being dissolved) per liter of solution. Molarity is one of the most common ways to express the concentration of a solution in chemistry. It is particularly useful when performing dilutions or mixing solutions to achieve desired concentrations, which are crucial in many chemical reactions and processes.

The fundamental formula for molarity is given by: \[ M = \frac{moles~of~solute}{liters~of~solution} \] To prepare a solution of a specific molarity, one must calculate the moles of the solute needed to dissolve in a given volume of solvent. And if we're diluting an existing solution, as in the textbook problem, it implies reducing the concentration by adding more solvent, which is often water.

It's important for students to remember that molarity is volume-dependent, which means that changes in temperature and pressure can affect the volume of the solution, and in turn, its concentration. Precision in measuring volume and mass ensures accurate preparation and dilution of solutions.

Chemistry Problem Solving

Problem solving in chemistry involves a systematic approach to dealing with chemical equations, calculations, and experimental data. It starts by identifying the known variables and what one needs to find. In the case of dilution problems, one must often employ the dilution equation: \[ C1 \times V1 = C2 \times V2 \] Here, \( C1 \) and \( V1 \) represent the concentration and volume of the concentrated solution, while \( C2 \) and \( V2 \) are the concentration and volume of the diluted solution we want to prepare.

By manipulating the formula and inserting the known values, as demonstrated in the problem, one can solve for the unknown variable. In this situation, rearranging the formula helped us find the required volume of concentrated NaOH needed to achieve the desired 3.00 M concentration in 3.50 L of solution. Enhanced understanding of these concepts leads to the development of critical thinking and the ability to apply knowledge to practical situations.

Safety considerations are also an integral part of chemical problem solving, especially when preparing solutions such as NaOH. Adequate personal protective equipment (PPE) like gloves and goggles must be used to prevent injury from chemical burns or exposure.