Question

If \(75 \mathrm{mL}\) of \(0.211 \mathrm{M} \mathrm{NaOH}\) is diluted to a final volume of \(125 \mathrm{mL}\), what is the concentration of \(\mathrm{NaOH}\) in the diluted solution?

Short answer

The concentration of NaOH in the diluted solution is \(0.1266 \mathrm{M}\).

Step-by-step solution

Write down the given values

Initial volume (V1) = 75 mL Initial concentration (C1) = 0.211 M Final volume (V2) = 125 mL Final concentration (C2) = ?

Use the formula to find the final concentration

We will use the formula: V1 × C1 = V2 × C2 Plugging in the given values: \(75 \mathrm{mL} \times 0.211 \mathrm{M} = 125 \mathrm{mL} \times C2\)

Solve for the final concentration (C2)

To find the final concentration C2, we need to solve for C2: \(C2 = \frac{75 \mathrm{mL} \times 0.211 \mathrm{M}}{125 \mathrm{mL}}\) \(C2 = \frac{15.825 \mathrm{mM}}{125 \mathrm{mL}}\)

Calculate and express the final concentration

Now, we can calculate the value of C2: \(C2 = 0.1266 \mathrm{M}\) Therefore, the concentration of NaOH in the diluted solution is \(0.1266 \mathrm{M}\).

Key concepts

Molarity

Molarity is a crucial concept in solution chemistry, referring to the concentration of a solution in terms of the amount of solute per volume of solution. It is expressed in moles per liter (M). To calculate the molarity of a solution, you need to know the number of moles of solute and the volume of the solution it is dissolved in. For example, if you have a 1 M solution, this means there is 1 mole of solute in every liter of solution.

To properly calculate the molarity of diluted and concentrated solutions, you can use the formula:

• Initial Molarity (C₁) × Initial Volume (V₁) = Final Molarity (C₂) × Final Volume (V₂)

This formula helps us keep track of the number of moles, which stays constant before and after the dilution.

Understanding molarity is fundamental for tasks such as preparing chemical solutions, carrying out experiments, and performing titrations in a lab setting.

Concentration

Concentration quantifies how much solute is present in a specific volume of solution. Alongside molarity, concentration can be measured using various units like mass percent, parts per million (ppm), and molality among others. However, molarity is one of the most commonly used units in chemistry because it directly relates to chemical reactions that occur in a liquid solution.

In the context of the problem we're examining, dilution affects concentration. When you add solvent to a solution, you increase its volume while the amount of solute remains unchanged. This results in a lower concentration. By using the relationship of volumes and molarities in dilution, chemists can predict the final concentration after dilution using the formula, keeping the moles of solute constant.

Remember, when performing dilution calculations, it is important to ensure that the units of volume used are consistent, typically in liters or milliliters.

Solution Chemistry

Solution chemistry is a field that involves studying homogenous mixtures where solute particles are dissolved in a solvent. Solutions are ubiquitous in both everyday life and scientific studies because a majority of chemical reactions occur in solutions.

Characteristics of solutions include their homogeneity and stability, meaning the composition is uniform throughout the mixture and it doesn't separate into different phases on standing. Key to understanding solution chemistry are concepts like solvent, solute, and the interactions between them. Solvents generally exist in greater quantity and dissolve the solutes, which are present in lesser amounts.

Dilution is a key process in solution chemistry, used to decrease the concentration of a solution by adding more solvent. It maintains the total number of moles of solute but increases the overall volume." If you're performing a dilution, the concepts of molarity and concentration come into play, ensuring that the relationship between the initial and final states of the solution is maintained. Knowing how to manipulate and calculate these properties effectively is essential for tasks such as making solutions with desired properties or adjusting the concentrations for experimental applications.