Repair a solution diagram using atoms, charge and concentration

Equal counts are not always a balanced solution

The first packet supplies 60 mmol CaCl₂ in a final 500 mL solution. The drawing starts with six Ca²⁺ symbols and six Cl⁻ symbols. Each symbol represents 10 mmol of the labeled species, not one molecule. Predict what is wrong before editing the chloride count.

The packet stipulates complete dissolution and dissociation. It is an original bookkeeping task, not a claim that the browser measured a preparation. Keep the six calcium symbols and build the chloride inventory. Check both element totals and net charge; do not rely on visual symmetry.

A solution need not be a liquid

A solution is homogeneous at the macroscopic scale: its composition and corresponding bulk properties do not systematically depend on the sampled region under the stated conditions. Gas mixtures and single-phase solid solutions can meet that definition, as can liquids. Not every alloy is a single homogeneous phase. A heterogeneous mixture has spatially different regions or phases; an overall average concentration can hide that variation. Solution states and uniformity, checked 31 October 2026.

Changed samples: Two equal-volume regions contain 0.10 and 0.30 mol/L of a constituent. Their pooled average is 0.20 mol/L. Does the average establish homogeneity? Conversely, must a uniform gas mixture be rejected as a solution because it is not liquid?

Check regional versus pooled evidence

The two different regional concentrations contradict the stated homogeneous composition despite their valid pooled average. A uniform gas mixture can be a solution; phase alone is not the criterion. Molecular fluctuations and measurement uncertainty should not be confused with a reproducible macroscopic composition gradient.

Two independent budgets

Each CaCl₂ formula amount supplies one calcium and two chlorines. Thus 60 mmol supplies 60 mmol Ca²⁺ and 120 mmol Cl⁻, or six and twelve symbols. Charges balance because 6×(+2)+12×(−1)=0 in symbol-charge units. The element ledger independently checks that all twelve chlorine atom units remain represented.

One atom unit represents 10 mmol of that element’s atoms. It is not the same as one species symbol when a species contains several atoms. For K₂SO₄, each sulfate ion contains one sulfur and four oxygens and has charge −2. Three sulfate symbols represent 30 mmol sulfate, 30 mmol sulfur atoms and 120 mmol oxygen atoms. The ion is not split into sulfur and oxygen ions in this stipulated dissolution model.

Repair the potassium sulfate packet. Six K⁺ symbols require three SO₄²⁻ symbols. Equal numbers of cations and anions are not required; total positive and negative charge must balance.

Neutrality alone cannot validate a drawing

In the sucrose packet, the solute remains neutral C₁₂H₂₂O₁₁ molecules. Any proposed count has net charge zero, including an empty or doubled inventory. Only the correct six symbols conserve the supplied carbon, hydrogen and oxygen amounts. Find a neutral but incorrect drawing and capture it before repairing the count.

This shows why the two checks are independent. Passing charge balance is not a substitute for conserving atoms. Passing this bounded atom-and-charge ledger also does not prove solubility, actual speciation or the quality of a written explanation.

Count species before dividing by final volume

For the repaired calcium chloride packet, analytical CaCl₂ concentration is 60/500=0.120 mol/L. That label counts the supplied compound formula amount. In the complete-dissociation model, [Ca²⁺]=0.120 mol/L and [Cl⁻]=120/500=0.240 mol/L. Brackets denote species concentration. The sum of these solute-species concentrations is 0.360 mol/L; it is not the concentration of water or a claim about osmotic behavior.

Switch to the packet diluted to final 1000 mL. Keep six calcium and twelve chloride symbols. The amounts are unchanged but their concentrations halve. The drawing is an inventory panel, deliberately not a volume scale: its fixed rectangle must not be interpreted as showing equal solution volumes. Read the supplied final-volume label and numerical concentration table.

The inherited molarity lesson explains final volume and unit conversion. The new action here is species-level accounting after dissociation, not repeating generic n/V arithmetic.

Transfer to two sources of the same ion

The mixed packet contains 30 mmol NaCl and 30 mmol CaCl₂ in final 500 mL. Construct the chloride count from both ingredients. The fixed cations are three Na⁺ and three Ca²⁺ symbols; the correct chloride inventory is nine symbols. Its concentration is 90/500=0.180 mol/L. Do not assume the final volume equals the sum of separately measured starting liquids; the final volume is supplied.

For an unfamiliar practice packet, replace calcium by magnesium and change amounts and volume. Preserve the counting logic rather than copying the previous numeric answer.

Hydration does not turn water into free hydrogen and oxygen ions

Water’s partly negative oxygen side tends to point toward a cation; partly positive hydrogen sides tend to point toward an anion. The diagram shows one representative orientation per ion, not a fixed coordination number or rigid hydration shell. The δ notation means partial charge within a neutral water molecule, distinct from the full ionic charges on Na⁺ or Cl⁻.

Mobile ions permit electrical conduction in a solution, whereas electrons carry current in a metal. Sucrose can dissolve without forming ions. These particle counts alone do not determine conductivity: mobility, interactions and experimental conditions also matter. Pure water’s small autoionization contribution is omitted here, so do not treat the sucrose model as an exact zero-conductivity measurement.

Sources and limits

• OpenStax electrolytes: dissociation, mobile ions and ion–dipole hydration.
• OpenStax dissolution: intact sucrose molecules and homogeneous solutions.
• AP Chemistry CED, 3.7.A and 3.8.A: solution quantities and particulate representations.

The packets assume complete dissolution and dissociation of the salts, molecular sucrose, homogeneous mixing and no reaction or precipitation. Ion pairing, activities and solubility limits require further evidence. The element ledger tracks solute atoms and omits solvent atoms. Your adjustable draft and captures are retained recipes; the original first construction is not locked automatically, and written reasoning is not graded by these checks.

Compare charge magnitude only under matched geometry

An ion’s full net charge can interact strongly with a polar molecule’s partial charges. Under comparable distance, orientation and partner conditions, ion–dipole attraction tends to exceed a corresponding interaction involving only partial charges. This is not a universal ranking of whole substances: separation, size, orientation, screening and competing contacts matter.

Original schematic comparison: Keep one water-like dipole’s geometry and distance fixed. Replace a nearby positively charged end with charge +0.25e by a point ion with charge +1e. In this deliberately simplified electrostatic comparison the dipole interaction energy is linear in the external charge. Predict the attractive energy magnitude, then explain why this does not rank two real solutions at different ion–water distances.

Check the controlled charge comparison

The magnitude is four times as large at exactly the stipulated identical geometry. Different distances, partner polarizability and collective solvent arrangements remove that simple comparison. The point-charge exercise explains a tendency, not a measured hydration energy or a claim that every ion–dipole interaction exceeds every hydrogen bond.

Intermolecular interactions, checked 31 October 2026.