Concentration And Molarity

Question

What mass of sodium hydroxide (NaOH) must be dissolved in 500 mL of water to prepare a 0.4 M solution? (Molar mass of NaOH = 40 g/mol)

RankGuru · Accepted Answer

Molarity is defined as the number of moles of solute dissolved per litre of solution. The formula is $M = n/V$, where $n$ is the number of moles and $V$ is the volume in litres. Rearranging: $n = M \times V = 0.4 \, \text{mol/L} \times 0.500 \, \text{L} = 0.2 \, \text{mol}$. Mass of NaOH required $= n \times M_r = 0.2 \times 40 = 8 \, \text{g}$. Option 4 g corresponds to only 0.1 mol, which would give a molarity of 0.2 M in 500 mL, not 0.4 M. Option 16 g corresponds to 0.4 mol, yielding 0.8 M in 500 mL. Option 20 g corresponds to 0.5 mol, giving 1.0 M in 500 mL. This is a direct application of the NCERT definition of molarity and solution preparation, a standard JEE and laboratory context. Plausibility check: 8 g of NaOH in 0.5 L gives $0.2 \, \text{mol}/0.5 \, \text{L} = 0.4 \, \text{M}$, confirming the answer is correct.

Concentration And Molarity

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