Question

If \(42.5 \mathrm{~g}\) of \(\mathrm{NaOH}\) is dissolved in water and diluted to a final volume of \(225 \mathrm{~mL}\), calculate the molarity of the solution.

Short answer

The molarity of the NaOH solution is 4.72 mol/L.

Step-by-step solution

Calculate moles of NaOH

To calculate the moles of NaOH, we need to divide its mass by its molar mass: Moles of NaOH = (mass of NaOH) / (molar mass of NaOH) The molar mass of NaOH = 22.989 (Na) + 15.999 (O) + 1.007 (H) = 39.997 g/mol Moles of NaOH = 42.5 g / 39.997 g/mol = 1.0625 mol

Convert the volume of the solution into liters

To convert the volume of the solution from mL to liters, simply divide the volume in mL by 1000: Volume of solution in liters = 225 mL / 1000 = 0.225 L

Calculate the molarity of the solution

Now that we have the moles of NaOH and the volume of the solution in liters, we can calculate the molarity: Molarity (M) = moles of solute / volume of solution in liters Molarity (M) = 1.0625 mol / 0.225 L = 4.72 M The molarity of the NaOH solution is 4.72 mol/L.

Key concepts

Moles of Solute

When it comes to understanding chemical solutions, the concept of moles of solute is crucial. A mole is a unit that measures an amount of substance in chemistry. One mole corresponds to Avogadro's number, which is approximately 6.022\(\times\)10^{23} particles, whether they're atoms, molecules, or ions.

In our exercise scenario, the moles of solute refers to the number of moles of sodium hydroxide (NaOH) present in the solution. To find this, divide the given mass of NaOH by its molar mass. The calculation bridges the gap between the macroscopic scale (grams) and the molecular scale (moles), and is fundamental to the study of stoichiometry, which deals with the quantitative relationships in chemical reactions.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's a bridge between the atomic and macroscopic worlds, as it allows chemists to count particles by weighing them. Determining the molar mass involves adding the atomic masses of all the atoms in a molecule. For example, the molar mass of NaOH is calculated using the atomic masses of sodium (Na), oxygen (O), and hydrogen (H) from the periodic table.

Importance in Calculations

In chemistry problems, knowing the molar mass of a substance allows you to convert between mass and moles, a key step in many quantitative analyses. This conversion is the foundation for many subsequent calculations, such as determining the moles of solute in a solution.

Solution Concentration

In chemistry, solution concentration tells us how much of a particular substance is dissolved in a given volume of solvent. It's one of the most common ways to express the composition of a solution. Molarity is a concentration term defined as the number of moles of solute per liter of solution, measured in moles per liter (mol/L).

This measurement provides critical information about the solution, such as its chemical potency and how it will react in various contexts like titrations or synthesis. Concentration concepts are not confined to academics but are also used in industries like pharmaceuticals, where precise dosages are essential.

Volume Conversion

Volume conversion is a simple yet vital step in many chemical calculations, particularly when working with solutions. In the context of molarity calculations, we often need to work in liters, the standard SI unit for volume. However, laboratory measurements might be provided in milliliters (mL) or other units.

Therefore, converting the volume of a solution to liters, as we must do in our exercise, is essential. The conversion factor is 1000 mL per 1 L. Remembering this relationship ensures that all the units match up correctly when performing calculations for molarity or other related exercises.

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products involved in chemical reactions. It's based on the conservation of mass and the concept of the mole. Being central to chemical equations and reactions, stoichiometry allows us to predict the outcomes of reactions, determine limiting reagents, and calculate the theoretical yield.

Understanding the stoichiometry behind a solution like NaOH helps us to relate the moles of solute to the volume and further to the concentration, encapsulating the essence of quantitative analysis in chemistry. Each stoichiometric calculation, as seen in this molarity calculation example, provides valuable practice for students and professionals in accurately determining the amounts of substances in chemical processes.