Question

If you wish to prepare a \(0.055 \mathrm{M}\) solution of \(\mathrm{NaNO}_{3}\), to what volume would you have to dilute \(25 \mathrm{~mL}\) of \(3.0 \mathrm{M} \mathrm{NaNO}_{3}\) ?

Short answer

To make a \(0.055 \mathrm{M}\) solution, the volume required will be approximately \(1364 \mathrm{~mL}\) or \(1.364 \mathrm{~L}\).

Step-by-step solution

Identify Knowns and Unknowns

The known quantities are: the initial molarity of the solution \(M_1=3.0 \mathrm{M}\), the volume of the concentrated solution \(V_1= 25 \mathrm{~mL}\), and the desired final molarity of the solution \(M_2 = 0.055 \mathrm{M}\). The unknown we're trying to solve for is the volume to which this solution must be diluted (\(V_2\)).

Apply the Dilution Formula

Use the formula for dilution to solve for \(V_2\): \(M_1V_1 = M_2V_2\). We can rearrange the formula to isolate \(V_2\): \(V_2 = \frac{M_1V_1}{M_2}\).

Substitute Values

Now substitute the given values in the formula for \(V_2\): \(V_2 = \frac{3.0 \mathrm{M} \times 25 \mathrm{~mL}}{0.055 \mathrm{M}}\).

Calculate the Result

Perform the arithmetic operation to get the result.

Key concepts

Molarity Calculation

Understanding molarity is essential when working with chemical solutions. It tells us the concentration of a solute within a given volume of solvent, and it is a fundamental concept in chemistry, particularly in solution preparation.

In the context of our example, molarity (\( M \) ) is defined as the number of moles of solute per liter of solution. Mathematically, it's expressed as: \( M = \frac{{moles \text{ of solute}}}{{volume \text{ of solution in liters}}} \) .

To find the molarity of a solution, you need to know the amount of substance (in moles) and the total volume of the solution (in liters). In the given exercise, the molarity calculation is integral to finding the final volume (\( V_2 \) ) after dilution.

Solution Preparation

Preparing chemical solutions of a desired concentration requires careful calculation and precise technique. It involves dissolving a specified amount of solute, often a solid, into a solvent, generally a liquid like water.

In our example, we started with a high concentration solution and aimed to dilute it to a lower concentration. To do so, we must add more solvent without adding more solutes. This process is common in laboratories when a less concentrated solution is needed for an experiment or procedure.

Tips for Accurate Solution Preparation:

• Always measure solute and solvent accurately.
• Ensure complete dissolution of the solute.
• Use volumetric flasks for precise volume measurements.
• Add the solute to the solvent, not the other way around, to aid in dissolution.

Concentration of Solutions

Concentration of a solution reflects how much solute is present in a given quantity of solvent. While molarity is a commonly used measure of concentration, there are other units as well, such as molality, weight percent, or volume percent. These different measures are used based on the nature of the solutions and the required precision.

In the textbook exercise, we focus on molarity to measure concentration. To alter the concentration of solutions, like diluting a sample, one can either add more solute to increase the concentration or add more solvent to decrease it. Calculation of the new concentration after dilution, using the initial molarity, the initial volume, and the final volume, is an everyday task for chemists.

The dilution formula (\( M_1V_1 = M_2V_2 \) ) relates the initial and final concentrations and volumes, allowing us to calculate unknown variables when preparing a specific concentration from an existing stock solution.