Question

Find the mass of sodium carbonate in grams to form 100 ml 0.1 M solution in water?
( Molar mass of \(\text{Na}_2\text{CO}_3\) = 106 g/mol)

• A. \(1.06\) g
• B. \(3.18\) g
• C. \(2.12\) g
• D. \(4.16\) g

Hint:

Moles = molarity x volume in litres, then multiply by the molar mass.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Molarity (M) is the number of moles of solute per litre of solution. So moles of solute = M x V (in litres), and mass = moles x molar mass.

Step 2: Key Formula or Approach
\[ n = M \times V_{(L)}, \qquad w = n \times M_{\text{molar}} \]

Step 3: Detailed Explanation
Volume \(V = 100 \text{ mL} = 0.1 \text{ L}\). Moles of \(\text{Na}_2\text{CO}_3\):
\[ n = 0.1 \times 0.1 = 0.01 \text{ mol} \]
Mass needed:
\[ w = 0.01 \times 106 = 1.06 \text{ g} \]
The other options come from using a wrong volume or wrong molar mass. For example, 3.18 g would be 0.03 mol and 2.12 g would be 0.02 mol, which would give 0.3 M and 0.2 M in 100 mL.

Final Answer:
Weighing 1.06 g of sodium carbonate and making the solution up to 100 mL gives 0.1 M. This is option (A). \[ \boxed{1.06 \text{ g}} \]