Problem 2 - Chemistry for Allied Health

Question

What is the molarity of a solution prepared with \(0.75\) moles \(\mathrm{NaCl}\) in \(250 . \mathrm{mL}\) solution?

Step-by-Step Solution

Answer

The molarity of the solution is 3 M.

Step 1: Understand Molarity

Molarity (m) is a measure of the concentration of a solute in a solution, expressed as moles of solute per liter of solution. The formula for molarity is given by:\[M = \frac{n}{V}\]where \(n\) is the number of moles of solute and \(V\) is the volume of solution in liters.

Step 2: Convert Volume to Liters

To use the molarity formula, the volume of the solution must be in liters. We have a volume of \(250\ mL\). Convert this to liters by dividing by 1000:\[V = \frac{250}{1000} = 0.250\ L\]

Step 3: Insert Values into Formula

Insert the given values of moles of NaCl (\(0.75\) moles) and the volume in liters (\(0.250\ L\)) into the molarity formula:\[M = \frac{0.75}{0.250}\]

Step 4: Calculate Molarity

Calculate the molarity by performing the division:\[M = 3\]This means the molarity of the solution is \(3\ M\).

Key Concepts

Solution Concentration

Solution concentration refers to the amount of solute present in a given volume of solution. It helps in understanding how strong or weak a solution is. Molarity is one of the most common ways to express solution concentration. It is calculated by taking the number of moles of solute and dividing it by the volume of the solution measured in liters. Commonly, concentration is expressed as:

• Molarity (M): moles of solute per liter of solution.
• Molality: moles of solute per kilogram of solvent.

Knowing the concentration of a solution is crucial in chemistry because it affects how a solution will react with others. Remember, for high precision in any calculation involving molarity, always ensure that your volume is accurately converted into liters and the amount of solute is measured in moles.

Moles of Solute

The concept of moles in chemistry serves as a bridge between the atomic scale and the macroscopic world. One mole is defined as exactly 6.022 x 10²³ particles (atoms, molecules, ions, etc.). Understanding moles:

• It allows chemists to count particles by weighing them.
• Helps in balancing chemical equations and performing stoichiometric calculations.

To find the moles of a solute in a solution, you need to know the amount (in grams) and the molar mass of the substance. In given exercises, such as calculating solution molarity, the moles of the solute might be directly provided or may need to be calculated using the formula:\[ n = \frac{m}{M} \]Where \( n \) is the moles, \( m \) is the mass in grams, and \( M \) is the molar mass in grams per mole.

Volume Conversion

Volume conversion is crucial when working with molarity because molarity calculation requires the volume to be in liters. Many problems provide the volume in milliliters, so converting to liters is a necessary step. Key points for volume conversion:

• 1 liter = 1000 milliliters (mL).
• Conversion from mL to L involves dividing the value by 1000.

For example, if a solution has a volume of 250 milliliters, converting it to liters involves performing the calculation:\[ V_{\text{liters}} = \frac{250}{1000} = 0.250 \text{ L} \]Always ensure the volume is in the correct units to ensure the accuracy of your molarity calculations.

Sodium Chloride Solution

Sodium Chloride (NaCl) is a common ionic compound often used in laboratory settings and real-world applications. When NaCl is dissolved in water, it dissociates into sodium (Na⁺) and chloride (Cl^-) ions. Characteristics of Sodium Chloride:

• Forms clear, colorless solutions when dissolved.
• Commonly known as table salt.
• Its solutions are often used in chemical reactions, testing, and as an electrolyte.

In preparing a sodium chloride solution for molarity calculations, ensure the following: - Precisely measure the solute and solvent volumes for accurate solution preparation. - Ensure the NaCl is fully dissolved for best results in any practical or experimental predicaments.