Q.German silver is a mixture of which metals?

Alloy Composition: Why the Formulas Work

Alloy composition is about how much of each metal is present in a mixture. The key formulas come from two simple ideas: mass conservation and volume additivity (approximately). Let's break down the reasoning.

1. Mass-Based Composition (Weight Percent)

The Formula

Why this holds

• Mass is conserved when metals are mixed. If you take 20 g of copper and 30 g of zinc, the total mass is exactly $20 + 30 = 50$ g.
• The fraction of copper is simply its share of the total mass: $\frac{20}{50} = 0.4$ or $40\%$.
• This is directly proportional — double the copper mass (keeping zinc fixed), and the weight percent doubles.

Key insight: Mass percent is the most reliable because mass doesn't change when metals are melted together (assuming no loss).

2. Atom-Based Composition (Atomic Percent)

The Formula

Why this holds

• Atoms are discrete particles. The number of atoms determines the alloy's properties at the atomic level (e.g., crystal structure).
• To convert from mass to moles:

• Example: 20 g of copper (atomic mass = 63.5 g/mol) gives $\frac{20}{63.5} \approx 0.315$ moles. 30 g of zinc (atomic mass = 65.4 g/mol) gives $\frac{30}{65.4} \approx 0.459$ moles.
• Total moles = $0.315 + 0.459 = 0.774$ Atomic percent of Cu = $\frac{0.315}{0.774} \times 100\% \approx 40.7\%$

Key insight: Atomic percent differs from weight percent because atoms have different masses. A heavy atom contributes more mass but not more atoms.

3. Volume-Based Composition (Volume Percent)

The Formula

Why this holds (approximately)

• Volume is not strictly additive — when metals mix, atoms may pack differently, causing slight volume changes (contraction or expansion).
• However, for many solid alloys, the volume change is small ($<1\%$), so we approximate:

• Volume of each metal = $\frac{\text{mass}}{\text{density}}$

Key insight: Volume percent is useful for porosity calculations or when density is critical (e.g., in casting), but it's less fundamental than mass or atomic percent.

4. Converting Between Composition Types

From weight percent to atomic percent …