Question

What mass of NaOH is contained in \(250.0 \mathrm{mL}\) of a \(0.400 \mathrm{M}\) sodium hydroxide solution?

Short answer

There are \(4.00\, \text{g}\) of NaOH contained in \(250.0\, \text{mL}\) of the \(0.400\, \text{M}\) sodium hydroxide solution.

Step-by-step solution

Identify the given values

We are given: - Volume of the solution: 250.0 mL - Molarity of the sodium hydroxide (NaOH) solution: 0.400 M

Convert the volume to liters

Before using the molarity formula, we need to convert the volume of the solution to liters. 1 L = 1000 mL, so we can use this conversion factor: Volume (L) = \(\frac{250.0\,\text{mL}}{1000\,\text{mL/L}} = 0.250\,\text{L}\)

Calculate the moles of NaOH

To find the moles of NaOH present in the solution, we need to use the molarity formula: Moles = Molarity x Volume Moles of NaOH = \(0.400\,\text{M}\) x \(0.250\,\text{L}\) = \(0.100\,\text{mol}\)

Calculate the molar mass of NaOH

We need to find the molar mass of NaOH to convert the moles to mass. To get the molar mass, find the atomic masses of the elements in NaOH using the periodic table: - Sodium (Na): 22.99 g/mol - Oxygen (O): 16.00 g/mol - Hydrogen (H): 1.008 g/mol Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.008 g/mol = 40.00 g/mol

Convert moles to mass

Now we can convert moles of NaOH to mass using the molar mass calculated in step 4: Mass of NaOH = Moles x Molar mass Mass of NaOH = \(0.100\,\text{mol}\) x \(40.00\,\text{g/mol}\) = \(4.00\,\text{g}\) So, there are 4.00 g of NaOH contained in 250.0 mL of the 0.400 M sodium hydroxide solution.

Key concepts

Mole Concept

Understanding the mole concept is fundamental to mastering chemistry, especially when dealing with chemical reactions and the quantification of substances. A mole is a unit of measurement that represents an immense quantity of particles, atoms, or molecules—specifically, Avogadro's number, which is approximately 6.022 x 10^23 entities.

When we calculate the number of moles, as shown in the exercise with sodium hydroxide (NaOH), we are essentially counting how many units of that substance we have. To grasp this, it may help to compare it to something more familiar, like a dozen. Just as a dozen represents 12 of something, a mole represents 6.022 x 10^23 of something.

To convert between moles and the number of particles, you can use Avogadro's constant. For example, if you have one mole of NaOH, you have 6.022 x 10^23 molecules of NaOH. This is crucial when you want to relate the macroscopic world that we can measure, like volume and mass, to the microscopic world of atoms and molecules that are too small to see or measure directly.

Concentration of Solution

The concentration of a solution is a measure of how much solute is dissolved in a given volume of solvent. Molarity, symbolized as M, is one of the most common units of concentration in chemistry. Molarity is defined as the number of moles of solute per liter of solution.

To calculate the concentration in terms of molarity, you divide the moles of solute by the volume of the solution in liters. For example, a 0.400 M NaOH solution contains 0.400 moles of sodium hydroxide per liter of solution. This becomes particular handy when you want to calculate the quantity of solute in a specific volume of solution, as you did with the exercise.

Improving Solution Concentration Understanding

When studying solutions, it's advisable to:

• Practice converting measurements like milliliters to liters since molarity depends on the volume in liters.
• Always associate molarity with the ratio moles/liter to solidify understanding.
• Use real-world examples, such as comparing concentrated fruit juice vs. diluted juice, to visualize concentration differences.

By considering these points, you can deepen your understanding of solution concentration and how it relates to everyday life.

Molar Mass

Molar mass is a term used to indicate the mass of one mole of any given substance. It is usually expressed in grams per mole (g/mol) and can be found by summing the atomic masses of all the atoms in a molecule of that substance. For instance, the molar mass of NaOH was determined by adding the atomic masses of sodium, oxygen, and hydrogen.

The molar mass is an essential link between the mass of a material you can measure on a scale and the intrinsic mole concept for counting particles chemically. Once you know the molar mass, you can convert from mass to moles or vice versa, which is a frequent requirement in chemical calculations, like the ones demonstrated in the exercise.

Relating Molar Mass to Real Applications

To solidify the understanding of molar mass, remember to:

• Get comfortable using the periodic table to find atomic weights.
• Regularly practice calculations converting mass to moles and moles to mass using the molar mass.
• Think of molar mass as the 'chemical bridge' that connects the tangible world (mass) with the theoretical world (moles).

With these tips, anyone can become proficient at using molar mass to navigate between the physical measurements and the chemical quantities required in various scientific and practical applications.