Question

A solution that is labeled "0.105 M NaOH" would contain _______ mol of \(\mathrm{NaOH}\) per liter of solution.

Short answer

A solution labeled "0.105 M NaOH" would contain 0.105 mol of NaOH per liter of solution.

Step-by-step solution

Understand the definition of molarity

Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute, in this case NaOH, divided by the volume of the solution, in liters: \[M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}\]

Rearrange the formula to solve for moles of solute

We are given the molarity of the NaOH solution, and we want to find the number of moles of NaOH per liter of solution. So, we need to rearrange the formula from Step 1 to solve for the number of moles: \[\text{moles of solute} = M \times \text{volume of solution (L)}\] Since we want to find the number of moles in one liter of solution, we will use the volume of 1 L.

Calculate the number of moles of NaOH

Now that we have our formula, we can plug in the given molarity (0.105 M) and the volume of 1 L of solution to find the number of moles of NaOH: \[\text{moles of NaOH} = (0.105 \,M) \times (1\, L) \] \[\text{moles of NaOH} = 0.105 \, mol\] So, a solution labeled "0.105 M NaOH" would contain 0.105 moles of NaOH per liter of solution.

Key concepts

Understanding Molarity

When studying chemistry, one will often come across the term 'molarity'. But what does it mean? Simply put, molarity is a way to express the concentration of a solution in terms of the amount of substance present in a given volume. It is denoted as 'M' and is calculated by dividing the moles of solute by the liters of solution.
To make it clearer, let's take a look at an analogy. Imagine you are making a batch of lemonade. The strength of the lemonade's flavor can be compared to the molarity of a solution - the more lemon juice (solute) you add to a certain volume of water (solvent), the stronger (more concentrated) your lemonade will be. In chemistry, if you have a 1 M solution, it means that there is 1 mole of solute in every liter of the solution. It's a straightforward way to understand how much solute is in a solution, and it is essential for experiments where precise concentrations are required.

The Role of Moles of Solute

The 'mole' is a fundamental concept in chemistry that represents a specific number of particles, whether they are atoms, molecules, ions, or other entities. One mole is equivalent to Avogadro's number (approximately 6.022 x 10²³) of particles. The number of moles of solute in a solution tells us the amount of that substance available for reaction or effect within the solution.
Calculating the moles of a solute is akin to counting the number of building blocks you have at hand; with this knowledge, you can scale recipes up or down or predict how much product you'll get from a reaction. Without understanding moles, you'd be guessing at how much solute is participating in your reactions, which in the precise world of chemistry, is simply not an option.

Concentration of a Solution

The concentration of a solution is an expression of how much solute exists within a certain volume of solvent. High concentration means that there is more solite in less solvent; low concentration indicates the opposite. This concept is critical for predicting how substances will interact in a solution.
Different units of concentration can include molarity, molality, and percent composition, among others. For students and scientists alike, knowing how to work with different units of concentration and convert between them is a basic but essential skill. It ensures the correct dosage of a drug, the proper chemical reactivity in a reaction, and even the flavor intensity in a culinary concoction.

Practical Application with a NaOH Solution

As an example of applying these concepts, let's consider a sodium hydroxide (NaOH) solution. Sodium hydroxide is a common alkaline compound used in many chemical reactions and industrial processes. It's often presented in a titration setup to determine the concentration of an acidic solution or used in cleaning products.
In the example given in the exercise, the molarity of the NaOH solution is 0.105 M. This information is telling us that each liter of this specific NaOH solution contains 0.105 moles of pure NaOH. By understanding how to compute and interpret molarity, you can handle various tasks such as adjusting solution concentrations, calculating the amount needed for neutralization reactions, and much more. It's a key component in successfully executing experiments and achieving predictable, accurate results in chemistry.