Problem 60 - Chemistry: The Central Science

Question

Your lab partner tells you that he has prepared a solution that contains \(1.50\) moles of \(\mathrm{NaOH}\) in \(1.50 \mathrm{~L}\) of aqueous solution, and therefore that the concentration of \(\mathrm{NaOH}\) is \(1.5 \mathrm{M}\). (a) Is he correct? (b) If not, what is the correct concentration?

Step-by-Step Solution

Answer

The lab partner is incorrect, as the concentration of NaOH is not 1.5 M. The correct concentration of NaOH in the solution is 1.0 M, calculated using the formula: Concentration (M) = \( \frac{1.50 \, moles \, NaOH}{1.50 \, L} \).

Step 1: Recall the concentration formula

The concentration of a solution can be found using the formula: Concentration (M) = moles of solute / volume of the solution (in liters) In this case, the solute is NaOH, and we are given the moles of NaOH and the volume of the solution.

Step 2: Calculate the concentration of NaOH

Plugging the provided values into the concentration formula, we can calculate the concentration of NaOH in the solution. Concentration (M) = \( \frac{1.50 \, moles \, NaOH}{1.50 \, L} \) Concentration (M) = 1.0 M

Step 3: Compare the calculated concentration to the claim

Now that we have calculated the concentration of NaOH in the solution to be 1.0 M, we can answer the two parts of the question. (a) Is he correct? No, our lab partner is not correct. Their claim of the concentration of NaOH being 1.5 M is incorrect. (b) What is the correct concentration? The correct concentration of NaOH in the solution is 1.0 M.

Key Concepts

Molarity

Molarity is a fundamental concept in chemistry, representing the concentration of a solution. It is defined as the number of moles of solute per liter of solution. The unit of molarity is moles per liter, often abbreviated as M. Understanding molarity is crucial for dilutions, chemical reactions, and calculating the amounts of reactants and products in a given reaction.

For example, if a solution has a molarity of 1 M, this means that there is one mole of the solute dissolved in every liter of the solution. Molarity is an intensive property, which means that it does not depend on the amount of solution; rather, it describes the ratio of solute to solvent in any given volume of solution.

Moles of Solute

The mole is a basic measurement unit in chemistry and is a way to count particles, such as atoms or molecules, in a given substance. One mole is equivalent to Avogadro's number (\(6.022 \times 10^{23}\) particles). In the context of solutions, 'moles of solute' refers to the number of moles of a substance (the solute) that are dissolved in a solvent to make a solution.

Calculating the moles of a solute is a straightforward process, generally involving the substance's molar mass and the mass of the solute used. This measurement allows scientists to understand how many particles of solute are present in a solution and to calculate molarity precisely.

Volume of Solution

The volume of solution in chemistry is the total amount of the solvent plus the solute that makes up the solution, and it is typically measured in liters (L) or milliliters (mL). The volume is a key factor when calculating the molarity of a solution. It's important to ensure accurate measurements of volume to get the correct concentration of a solution. People often use volumetric flasks, graduated cylinders, or pipettes in the lab for accurate measurements.

When calculating molarity, the volume must be in liters to align with the standard unit for molarity, which is moles per liter. If volume measurements are taken in milliliters, they need to be converted to liters by dividing by 1000.

Concentration Formula

The concentration formula is a quick and simple way to calculate the molarity of a solution. The formula is written as:\[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]By using this formula, you can calculate the molarity of a solution if you are given the moles of solute and the volume of the solution. For example, to find the molarity of a sodium hydroxide (\text{NaOH}) solution with 1.50 moles of \text{NaOH} dissolved in 1.50 liters of solution, the molarity would be 1.0 M since:\[ \text{Molarity} (M) = \frac{1.50 \, \text{moles} \, \text{NaOH}}{1.50 \, \text{L}} = 1.0 \, \text{M} \]It's essential to ensure that the volume is in liters when using this formula, as molarity is defined per liter of solution.