Alcohol of mass 21g and density 0.7g cm-3 is mixed with 10g of water. Determine the density of the mixture [density of water = 1.0gcm-3]

Analyze the question: We are mixing two liquids and need the density of the mixture. The key idea is that density of mixture = total mass ÷ total volume (assuming the volumes simply add).

Concept: Density = mass / volume, so Volume = mass / density.

Solution:

Alcohol:

• Mass = 21 g, density = 0.7 g/cm³
• Volume = 21 / 0.7 = 30 cm³

Water:

• Mass = 10 g, density = 1.0 g/cm³
• Volume = 10 / 1.0 = 10 cm³

Mixture:

• Total mass = 21 + 10 = 31 g
• Total volume = 30 + 10 = 40 cm³

Density of mixture = 31 / 40 = 0.775 g/cm³

Answer: Option A, 0.775 g/cm³.

Tip: For mixture problems, never average the densities directly. Always find each volume first (V = m/ρ), then divide total mass by total volume. Here, a simple average of 0.7 and 1.0 would give 0.85, which is wrong, because the amounts are not equal.