Question

The molarity of the solution prepared by dissolving \(6.3\text{ g}\) of oxalic acid (\(\text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O}\)) in \(250\text{ mL}\) of water in mol L\(^{-1}\) is \(x \times 10^{-2}\). The value of \(x\) is \(\dots\dots\dots\). (Nearest integer)
[Atomic mass : H : 1.0, C : 12.0, O : 16.0]

Hint:

Always include the water of crystallisation when calculating the molar mass of hydrated crystals like oxalic acid or Mohr's salt.

Answer 1

Correct Answer: 20

Step 1: Understanding the Concept:
Molarity (\(M\)) is defined as the number of moles of solute dissolved in one litre of solution.
Step 2: Key Formula or Approach:
\[ \text{Molarity } (M) = \frac{\text{moles of solute}}{\text{Volume of solution in Litres}} \]
\[ \text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Step 3: Detailed Explanation:
1. Calculation of Molar Mass of Hydrated Oxalic Acid (\(\text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O}\)):
\[ \text{Molar mass} = 2(1.0) + 2(12.0) + 4(16.0) + 2[2(1.0) + 16.0] \]
\[ \text{Molar mass} = 2 + 24 + 64 + 2(18) = 90 + 36 = 126\text{ g/mol} \]
2. Calculation of Moles:
\[ \text{Moles} = \frac{6.3\text{ g}}{126\text{ g/mol}} = 0.05\text{ mol} \]
3. Calculation of Molarity:
Volume = \(250\text{ mL} = 0.25\text{ L} \).
\[ M = \frac{0.05\text{ mol}}{0.25\text{ L}} = 0.2\text{ mol/L} \]
4. Finding the value of \(x\):
The question states Molarity = \(x \times 10^{-2}\).
\[ 0.2 = 20 \times 10^{-2} \implies x = 20 \]
Step 4: Final Answer:
The value of \(x\) is 20.