Calculating Molarity of NaOH Solution

The question asks us to calculate the molarity of a solution. Molarity is a common way to express the concentration of a solution. It is defined as the number of moles of solute dissolved per liter of solution.

Understanding Molarity

Molarity (M) is calculated using the following formula:

\( \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in Liters}} \)

In this problem, the solute is Sodium Hydroxide (NaOH), and the solvent is implied to be water, forming an aqueous solution with a total volume of 450 mL.

Step-by-Step Calculation of Molarity

Step 1: Identify the given quantities

• Mass of solute (NaOH) = 5 g
• Volume of solution = 450 mL

Step 2: Calculate the molar mass of the solute (NaOH)

To find the number of moles, we first need the molar mass of NaOH. The atomic masses are approximately:

• Sodium (Na): 23 g/mol
• Oxygen (O): 16 g/mol
• Hydrogen (H): 1 g/mol

Molar mass of NaOH = Molar mass of Na + Molar mass of O + Molar mass of H

\( \text{Molar mass of NaOH} = 23 \text{ g/mol} + 16 \text{ g/mol} + 1 \text{ g/mol} = 40 \text{ g/mol} \)

Step 3: Calculate the number of moles of NaOH

The number of moles is calculated by dividing the mass of the solute by its molar mass.

\( \text{Number of moles of NaOH} = \frac{\text{Mass of NaOH}}{\text{Molar mass of NaOH}} \)

\( \text{Number of moles of NaOH} = \frac{5 \text{ g}}{40 \text{ g/mol}} \)

\( \text{Number of moles of NaOH} = 0.125 \text{ moles} \)

Step 4: Convert the volume of the solution from milliliters (mL) to liters (L)

The molarity formula requires the volume in liters. There are 1000 mL in 1 L.

\( \text{Volume of solution in Liters} = \text{Volume in mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} \)

\( \text{Volume of solution in Liters} = 450 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} \)

\( \text{Volume of solution in Liters} = 0.450 \text{ L} \)

Step 5: Calculate the molarity of the solution

Now we can use the molarity formula with the calculated moles of solute and the volume of the solution in liters.

\( \text{Molarity (M)} = \frac{\text{Number of moles of NaOH}}{\text{Volume of solution in Liters}} \)

\( \text{Molarity (M)} = \frac{0.125 \text{ moles}}{0.450 \text{ L}} \)

\( \text{Molarity (M)} \approx 0.2777... \text{ M} \)

Rounding to three significant figures, the molarity is approximately 0.278 M.

Comparing with Options

Let's compare our calculated molarity with the given options:

• 1. \( 0.278 \times 10^{-3} \text{ M} \) (This is 0.000278 M)
• 2. \( 0.278 \text{ M} \)
• 3. \( 2.78 \times 10^{-3} \text{ M} \) (This is 0.00278 M)
• 4. \( 2.78 \text{ M} \)

Our calculated value, 0.278 M, matches Option 2.

Revision Table: Key Concepts for Molarity Calculation

Additional Information: Solution Concentration Units

Molarity is just one way to express the concentration of a solution. Other common concentration units include:

• Molality (m): Moles of solute per kilogram of solvent. (Molality is less common than molarity in everyday lab work but is useful because it is independent of temperature changes).
• Mass Percent (% w/w): (Mass of solute / Mass of solution) × 100%.
• Volume Percent (% v/v): (Volume of solute / Volume of solution) × 100%.
• Mole Fraction (X): Moles of component / Total moles of all components in the solution.

Each unit is useful in different contexts and for different types of calculations in chemistry.