Q.Calculate the molarity of a solution containing 5 g of NaOH in 450 mL solution.

The key idea is Molarity Calculation.

Molarity ($M$) is defined as the number of moles of solute per liter of solution. First, calculate the molar mass of NaOH and then the moles of NaOH. Convert the given volume of the solution from milliliters to liters. Finally, divide the moles of NaOH by the volume of the solution in liters.

1. The molar mass of NaOH is $23 (\text{Na}) + 16 (\text{O}) + 1 (\text{H}) = 40 \text{ g/mol}$.
2. Moles of NaOH = $\frac{\text{Mass}}{\text{Molar Mass}} = \frac{5 \text{ g}}{40 \text{ g/mol}} = 0.125 \text{ mol}$. …

Molarity is a fundamental concept in chemistry used to express the concentration of a solution. It tells us how many moles of a solute are dissolved in one liter of the entire solution. Understanding this definition is key to solving such problems. We need to find two main quantities: the number of moles of the solute (NaOH) and the total volume of the solution in liters.

Here's how we approach the calculation:

1. Identify the given information and the goal.

   We are given:

   • Mass of solute (NaOH) $= 5 \text{ g}$
   • Volume of solution $= 450 \text{ mL}$ We need to calculate the molarity ($M$) of the solution.

2. Calculate the molar mass of the solute (NaOH).

   To convert the mass of NaOH into moles, we first need its molar mass. We sum the atomic masses of its constituent elements:

   • Atomic mass of Na $= 22.99 \text{ g/mol}$
   • Atomic mass of O $= 16.00 \text{ g/mol}$
   • Atomic mass of H $= 1.01 \text{ g/mol}$

   Molar mass of NaOH $= (22.99 + 16.00 + 1.01) \text{ g/mol} = 40.00 \text{ g/mol}$

3. Calculate the number of moles of NaOH.

   Now that we have the mass of NaOH and its molar mass, we can find the number of moles using the formula:

   $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$

   Moles of NaOH $= \frac{5 \text{ g}}{40.00 \text{ g/mol}} = 0.125 \text{ mol}$

4. Convert the volume of the solution from milliliters to liters.

   Molarity is defined as moles per liter of solution. The given volume is in milliliters, so we must convert it to liters.

   We know that $1 \text{ L} = 1000 \text{ mL}$. …

Method: Molarity Formula Method

Molarity ($M$) is defined as the number of moles of solute per litre of solution.

Formula

Steps

Step 1: Find moles of NaOH

• Molar mass of NaOH = $23 + 16 + 1 = 40 \text{ g/mol}$
• Moles of NaOH = $\frac{\text{mass}}{\text{molar mass}} = \frac{5}{40} = 0.125 \text{ mol}$

Step 2: Convert volume to litres

• Volume given = 450 mL
• In litres: $\frac{450}{1000} = 0.45 \text{ L}$

Step 3: Apply the molarity formula …

Here are the most common mistakes students make when solving this exact problem, along with the conceptual fix for each.

Mistake 1: Confusing Molarity with Molality

• The Error: Students see "5 g" and "450 mL" and immediately plug numbers into the molality formula ($m = \frac{\text{moles of solute}}{\text{kg of solvent}}$). They treat the 450 mL as the mass of the solvent in grams.
• Why it happens: The words "molarity" and "molality" sound similar, and both start with "mol". In a hurry, the brain defaults to the wrong formula.
• How to avoid it: Always write the definition first.
  • Molarity ($M$) = $\frac{\text{moles of solute}}{\text{liters of solution}}$
  • Molality ($m$) = $\frac{\text{moles of solute}}{\text{kg of solvent}}$
  • The key difference: Molarity uses total solution volume; Molality uses solvent mass. In this problem, you are given 450 mL of solution, not solvent. Therefore, you must use the Molarity formula.

Mistake 2: Forgetting to Convert mL to Liters

• The Error: Students plug 450 directly into the formula: $M = \frac{0.125 \text{ mol}}{450} = 0.00027 \text{ M}$.
• Why it happens: The formula requires volume in liters, but the problem gives volume in milliliters. It’s a simple unit mismatch.
• How to avoid it: Convert before you calculate.
  • $450 \text{ mL} = 450 \times 10^{-3} \text{ L} = 0.45 \text{ L}$
  • Now the calculation becomes: $M = \frac{0.125}{0.45} = 0.278 \text{ M}$.
  • Pro tip: Write the unit (L) next to the number in your formula to catch this error.

Mistake 3: Using the Wrong Molar Mass

• The Error: Students use the molar mass of Na (23 g/mol) or O (16 g/mol) or H (1 g/mol) individually, instead of adding them up for NaOH.
• Why it happens: They rush and don't sum the atomic masses of all atoms in the compound.
• How to avoid it: Always calculate the molar mass of the entire compound first.
  • NaOH: Na (23) + O (16) + H (1) = 40 g/mol
  • Moles of NaOH = $\frac{5 \text{ g}}{40 \text{ g/mol}} = 0.125 \text{ mol}$
  • Double-check: Write the formula and add each atomic mass once. …