What is the concentration of a solution containing 2g of NaOH in 100cm3 of solution? [Na=23, O=16, H=1]

Analysis

To find the concentration of the solution, we need to determine the number of moles of the solute (NaOH) and divide it by the volume of the solution in cubic decimeters ($dm^3$).

Concept

1. Molar Mass Calculation: First, find the molar mass of NaOH by summing the atomic masses of its constituent elements.
2. Mole Calculation: Use the formula: $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$.
3. Volume Conversion: Since the volume is given in $cm^3$, convert it to $dm^3$ by dividing by 1000 ($1000 cm^3 = 1 dm^3$).
4. Concentration Calculation: Use the formula: $\text{Concentration (mol/dm}^3) = \frac{\text{Moles}}{\text{Volume in dm}^3}$.

Step-by-Step Solution

Step 1: Calculate the Molar Mass of NaOH

• Na = 23, O = 16, H = 1
• Molar Mass of NaOH = $23 + 16 + 1 = 40 \text{ g/mol}$

Step 2: Calculate the number of moles of NaOH

• $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$
• $\text{Moles} = \frac{2 \text{ g}}{40 \text{ g/mol}} = 0.05 \text{ moles}$

Step 3: Convert volume from $cm^3$ to $dm^3$

• $\text{Volume} = \frac{100 cm^3}{1000} = 0.1 dm^3$

Step 4: Calculate the concentration

• $\text{Concentration} = \frac{\text{Moles}}{\text{Volume in dm}^3}$
• $\text{Concentration} = \frac{0.05 \text{ mol}}{0.1 dm^3} = 0.5 \text{ mol/dm}^3$

Conclusion

Comparing our result to the given options, the concentration is $0.50 \text{ mol/dm}^3$. This matches option C.

Exam Tip

Always watch your units! JAMB examiners love to give volumes in $cm^3$ to see if you remember to convert to $dm^3$ (by dividing by 1000) before calculating molarity. A common mistake is to divide by 100 instead of 1000.