Molarity Calculation Explained

The question asks us to find the molarity of a solution containing Sodium hydroxide (NaOH). Molarity is defined as the number of moles of solute dissolved per liter of solution. To calculate molarity, we need two things: the number of moles of NaOH and the volume of the solution in liters.

Sodium Hydroxide Molar Mass

First, let's calculate the molar mass of Sodium hydroxide (NaOH). We are given the atomic weights:

• Sodium (Na) = 23
• Oxygen (O) = 16
• Hydrogen (H) = 1

The molar mass of NaOH is the sum of the atomic weights of its constituent atoms:

Molar mass of NaOH $ = $ Atomic weight of Na $ + $ Atomic weight of O $ + $ Atomic weight of H

Molar mass of NaOH $ = 23 + 16 + 1 = 40 $ g/mol

Moles of NaOH

Next, we need to find the number of moles of NaOH present in the solution. We are given that the mass of NaOH is 5 grams.

The formula to calculate the number of moles is:

Number of moles $ = \frac{\text{Mass of substance}}{\text{Molar mass of substance}}$

Substituting the values:

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

Number of moles of NaOH $ = 0.125 $ moles

Solution Volume in Liters

The volume of the solution is given in millilitres (mL), but molarity requires the volume in litres (L). We need to convert 500 millilitres to litres.

There are 1000 millilitres in 1 litre.

Volume in litres $ = \frac{\text{Volume in millilitres}}{1000}$

Volume of solution $ = \frac{500 \text{ mL}}{1000 \text{ mL/L}} = 0.5 \text{ L}$

Calculating Molarity

Now we have the number of moles of NaOH (0.125 mol) and the volume of the solution in liters (0.5 L). We can calculate the molarity using the formula:

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

Molarity $ = \frac{0.125 \text{ mol}}{0.5 \text{ L}}$

Molarity $ = 0.25 $ mol/L

So, the molarity of the solution is 0.25 mol/litre.

Let's check the options:

1. 0.0625 mol/litre
2. 0.5 mol/litre
3. 0.025 mol/litre
4. 0.25 mol/litre

The calculated molarity matches option 4.