How many grammes of NaOH(s) would be needed to produce 100.0 cm3 of a 0.20 mol $dm^{-3}$ NaOH, (aq)? [NaOH = 40.0]

Step 1: Analyze the question We need the mass of NaOH required to make 100.0 cm³ of solution with a concentration of 0.20 mol/dm³.

Step 2: Concept

• Moles = concentration × volume (in dm³)
• Mass = moles × molar mass

Step 3: Solution

Convert the volume to dm³: 100.0 cm³ = 100.0 ÷ 1000 = 0.100 dm³

Moles of NaOH: n = C × V = 0.20 × 0.100 = 0.020 mol

Mass of NaOH: mass = n × M = 0.020 × 40.0 = 0.80 g

Step 4: Answer The mass needed is 0.80 g, which is option D.

Why the other options are wrong:

• A (800 g): the volume was not converted from cm³ to dm³.
• B (0.02 g): this is the number of moles, and the student forgot to multiply by the molar mass.
• C (20.0 g): this comes from a wrong conversion, such as using 100 dm³ in place of 0.1 dm³.

Tip: Always convert cm³ to dm³ first by dividing by 1000. Then follow the chain: C × V → moles → × M → mass. A quick shortcut is mass = C × M × V, so 0.20 × 40 × 0.1 = 0.80 g.