Question

You need to make \(150.0 \mathrm{mL}\) of a \(0.10-M\) NaCl solution. You have solid NaCl, and your lab partner has a \(2.5-M\) NaCl solution. Explain how you each make the 0.10-M NaCl solution.

Short answer

To make a $0.10 \, \text{M}$ NaCl solution using solid NaCl, dissolve \(mass = (0.10 \,\text{M})(0.150 \,\text{L})(58.44 \,\text{g/mol})\) of solid NaCl in enough water to make a total volume of $150.0 \, \text{mL}$. To make the same solution using the $2.5 \, \text{M}$ NaCl solution, take an initial volume \(V1 = \frac{(0.10\,\text{M})(0.150 \,\text{L})}{2.5 \, \text{M}}\) and dilute it to a total volume of $150.0 \, \text{mL}$ with water.

Step-by-step solution

Calculate the moles of NaCl needed for the 0.10-M NaCl solution

Firstly, we need to find out the number of moles of NaCl required for creating a 0.10-M NaCl solution with a volume of 150.0 mL. To do this, we will use the molarity formula: Molarity (M) = moles of solute (n) / volume of solution (L) Rearrange the formula to solve for the moles of NaCl: moles of solute (n) = Molarity (M) × volume of solution (L) Since the volume is given in mL, it needs to be converted to L: Volume in L = 150.0 mL × (1 L / 1000 mL) = 0.150 L Now, calculate the moles of NaCl: \(n = (0.10 \,\text{M}) \times (0.150 \,\text{L})\)

Calculate the mass of solid NaCl needed

Now that we have the moles of NaCl required, we can calculate the mass of the solid NaCl needed. The molecular weight of NaCl is 58.44 g/mol. To find the mass of NaCl, multiply the moles of NaCl by its molecular weight: Mass of NaCl (g) = moles of NaCl × molecular weight of NaCl \(mass = (n) \times (58.44 \,\text{g/mol})\)

Making the 0.10-M NaCl solution with the solid NaCl

To make the 0.10-M NaCl solution, simply dissolve the calculated mass of solid NaCl in enough water to make a total volume of 150.0 mL.

Diluting the 2.5-M NaCl solution to make the 0.10-M NaCl solution

To dilute the 2.5-M NaCl solution to create the 0.10-M NaCl solution, use the dilution formula: C1V1 = C2V2 Here, C1 is the initial concentration of the solution (2.5-M), V1 is the initial volume of the solution we want to find, C2 is the final concentration of the solution (0.10-M), and V2 is the final volume of the solution (150.0 mL). Rearrange the formula to find the initial volume (V1): V1 = (C2V2) / C1 Convert the volume in mL to L: V2 in L = 150.0 mL × (1 L / 1000 mL) = 0.150 L Now, calculate the volume V1: \(V1 = \frac{(0.10 \,\text{M})(0.150 \,\text{L})}{2.5 \,\text{M}}\)

Making the 0.10-M NaCl solution by diluting the 2.5-M NaCl solution

To make the 0.10-M NaCl solution from the 2.5-M NaCl solution, measure the calculated volume (V1) and dilute it to a total volume of 150.0 mL with water.

Key concepts

Dilution

Dilution is a process used in chemistry to decrease the concentration of a solute in a solution. When you have a concentrated solution and you need a solution with a lower concentration, dilution is your go-to method.
Essentially, you add more solvent to the solution. This increases the solution's total volume, while the amount of solute remains the same. Consequently, the concentration of the solute decreases.
To calculate how much of the concentrated solution you need to dilute, you use the dilution formula:

• \( C_1V_1 = C_2V_2 \)
• Here, \( C_1 \) is the initial concentration, \( V_1 \) is the volume of the concentrated solution, \( C_2 \) is the target concentration, and \( V_2 \) is the target volume.

This formula helps determine the volume of the concentrated solution needed to achieve the desired dilution. The process of dilution keeps the moles of solute constant but increases the volume of solution.

Sodium Chloride Solution

Sodium chloride, commonly known as table salt, is an ionic compound comprising sodium (Na) and chlorine (Cl). Solutions of sodium chloride are frequently used in chemistry.
One of the key aspects to understanding sodium chloride solutions is molarity. Molarity is the number of moles of solute per liter of solution, and it's represented with the unit M (moles per liter).
When preparing a sodium chloride solution, the right concentrations are crucial. For example, if you're creating a 0.10-M NaCl solution, you will measure the necessary amount of NaCl and dissolve it in water to achieve this concentration.
Whether you're starting with solid NaCl or a more concentrated NaCl solution, calculating the correct amount or dilution will ensure the desired concentration.

Moles Calculation

Moles are a fundamental concept in chemistry for quantifying the amount of a substance. A mole is a unit that represents \(6.022 \times 10^{23}\) entities, which could be atoms, molecules, or ions.
Calculating moles involves the molarity equation:

• Molarity (M) = moles of solute (n) / volume of solution (L)
• Rearranged, it becomes: \( n = M \times V \)

By using this relation, you can calculate the amount of moles in a specific volume of a given molarity solution. For example, if you have a 0.10-M solution in 0.150 L, you would multiply the two to find the moles of solute. Knowing the moles helps in determining the amount needed for reactions or solutions.