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Hydrometallurgy fundamentals · Module 1 · 1.2

Solution density and why it matters

Density is the bridge between the mass a circuit balances and the volume it meters. How it moves with concentration and temperature, and what it costs to assume it constant.

TypeLearning topic — professional and student · shared spine

The idea

Density is the most quietly load-bearing property in a hydromet circuit. It is the conversion between the volumes a plant flows and meters and the masses an engineer balances. Every time a flow in cubic metres per hour becomes a mass in tonnes per hour, density did the work; every time a wt% becomes a g/L, density was the bridge. Treat it as a constant and the error propagates into assays, inventories and balances all at once.

Why density matters

Three things make density matter in practice.

  • Assays: a metal concentration read as g/L only converts to a saleable mass through the solution density.
  • Flow and inventory: a tank holding a known volume holds a mass that depends on density, and a pump sized on volumetric flow moves a mass that does too.
  • Process control: density is often the cheapest online proxy for concentration — a nucleonic or differential-pressure density gauge stands in for a titration — but only if the density-to-concentration relation is known and current.

How density moves

Density moves with two variables, and both matter. It rises with concentration: dissolve more salt or acid into water and the solution gets heavier, often steeply, so a strong liquor can be a third again as dense as water. It falls with temperature: warm a solution and it expands and lightens, a smaller effect than concentration but enough to matter when a hot leach liquor is metered against a cold standard. A density quoted without its temperature is half a number. This is why the substance hubs here tabulate density on a grid of concentration and temperature rather than as a single figure — the property is a surface, not a point.

The cost of assuming density constant is concrete. Read a 50 wt% sulfuric liquor as if a litre weighed a kilogram and you understate its mass by a third — the acid is nearly 1400 kg/m³, not 1000. Carry that into a reagent balance and the acid account is wrong by the same third. The discipline is the opposite habit: never let a volume become a mass without a density that matches the solution’s strength and temperature, and never trust a g/L figure whose underlying density you cannot name.

The worked thread below makes the point with two committed grid nodes from the sulfuric-acid hub: the same volumetric flow carries very different masses at different strengths, and the gap is entirely the density. The hubs for sulfuric acid, caustic and copper sulfate give you those density surfaces directly.

Diagram

H₂SO₄ density vs concentration at 20 °C — committed grid1032166857520 wt% · 1140.4 kg/m³50 wt% · 1396.7 kg/m³concentration (wt%)density ρ (kg/m³)

Now run it

  • Read the acid density at two strengths and the same temperature to see how steeply density climbs with concentration.

  • Compare caustic density across its concentration grid to size the mass behind a metered volume.

  • Read tankhouse-electrolyte density against concentration and temperature where density stands in for an assay.

Worked thread

A pump moves 100 m³/h of sulfuric liquor. Read two committed density nodes at the same temperature and find how much more mass the stronger liquor carries.

  1. 01Weak node: H₂SO₄ 20 wt% at 20 °C = 1140.4 kg/m³ (sulfuric-acid.json grid).
  2. 02Strong node: H₂SO₄ 50 wt% at 20 °C = 1396.7 kg/m³ (same grid).
  3. 03Mass flow, weak: 100 m³/h × 1140.4 kg/m³ = 114 040 kg/h = 114.04 t/h.
  4. 04Mass flow, strong: 100 m³/h × 1396.7 kg/m³ = 139 670 kg/h = 139.67 t/h.
  5. 05Difference: 139.67 − 114.04 = 25.63 t/h.
Result

At one volumetric flow, the 50 wt% liquor carries 25.63 t/h more mass than the 20 wt% — the density node, nothing else, sets the gap.

Source

sulfuric-acid.json committed density grid (20 wt% and 50 wt%, both at 20 °C).

Sources

  • Perry, R.H. & Green, D.W. (eds.), Perry’s Chemical Engineers’ Handbook, 8th ed., 2008.
  • Lide, D.R. (ed.), CRC Handbook of Chemistry and Physics, 89th ed., 2008.
  • Laliberté, M. & Cooper, W.E., Model for Calculating the Density of Aqueous Electrolyte Solutions, J. Chem. Eng. Data, 2004.

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