Antifreeze Batch for a Desert Workshop Fleet
A garage in Jodhpur services radiator cooling systems. The workshop buys ethylene glycol (molar mass 62 g mol⁻¹) in bulk and adds it to 4.0 kg of water in each aluminium radiator; K_f for water is 1.86 K kg mol⁻¹. The owner wants protection down to −15 °C, and insists the mixture must also stay pumpable, so no more than about 35% glycol by mass is acceptable. A rival supplier offers ready-made coolant containing 30% ethylene glycol by mass, and a third option is rock salt (NaCl, molar mass 58.5 g mol⁻¹), which a neighbouring workshop uses because it is cheap. The apprentice argues that salt is better because "half as many moles are needed since each NaCl gives two particles". Records show the local water is hard and the radiators are aluminium with copper cores. Last winter one radiator in the fleet cracked after the coolant was diluted with tap water.
1. Calculate the ethylene glycol requirement for one radiator and decide whether the owner's 35% by mass ceiling is satisfied. State your assumptions and comment on the margin.
Read the worked answer
Depression needed: ΔT_f = 0 − (−15) = 15 K.
Molality: m = ΔT_f / K_f = 15 / 1.86 = 8.06 mol kg⁻¹. Molality is per kg of solvent, so divide by 4.0 kg of water, not by the total mass.
Moles and mass: n = 8.06 × 4.0 = 32.3 mol; mass = 32.3 × 62 ≈ 2.0 × 10³ g ≈ 2.0 kg.
Mass fraction: 2.0 / (2.0 + 4.0) = 0.33, i.e. 33% - inside the 35% limit, but not by much.
Margin check: at the 35% ceiling the mixture contains 0.565 mol glycol per 65 g water = 8.7 mol kg⁻¹, giving ΔT_f ≈ 16.2 K, so the best protection the owner's own viscosity rule allows is about −16 °C. The two constraints are only just compatible, and any error in the glycol charge eats the margin.
Assumptions: glycol is a non-volatile non-electrolyte (i = 1) and the solution is ideal-dilute; real glycol–water mixtures deviate, so the practical freezing point should be confirmed with a hydrometer rather than trusted from the formula.
2. The apprentice proposes rock salt instead. Compute the mass that would be needed and give chemistry-based reasons why the workshop should still refuse it.
Read the worked answer
The arithmetic: the freezing point depends on the number of particles, and NaCl gives two ions per formula unit, so the required particle amount is unchanged.
n(particles) = 32.3 mol → n(NaCl) = 32.3 / 2 = 16.1 mol → mass = 16.1 × 58.5 ≈ 944 g ≈ 0.94 kg.
So the apprentice is right that it is lighter and cheaper. The refusal is chemical, not arithmetic:
- Solubility limit. NaCl dissolves only to about 6 mol kg⁻¹ near 0 °C, but the calculation demands 16.1 mol in 4.0 kg, i.e. ≈4 mol kg⁻¹… and once the bath cools toward the eutectic the salt crystallises and blocks the core tubes. Reaching −15 °C reliably with brine is impossible in practice.
- Chloride attack. Chloride breaks down the protective Al₂O₃ film on the aluminium, causing pitting.
- Galvanic couple. Aluminium body plus copper core in a conducting brine makes a cell in which aluminium is the anode (E° ≈ −1.66 V) and corrodes sacrificially; chloride accelerates it.
- Hard water. Ca²⁺ and Mg²⁺ already present precipitate as carbonates on hot surfaces; salt adds no corrosion inhibitor and gives almost no boiling-point protection.
Verdict: glycol, with distilled water.
3. The supplier's ready-mixed coolant is 30% glycol by mass. Will it protect to −15 °C? And what does the cracked radiator tell you about how the fleet is being maintained?
Read the worked answer
Test the claim: take 100 g of coolant → 30 g glycol and 70 g water. n = 30 / 62 = 0.484 mol; m = 0.484 / 0.070 = 6.91 mol kg⁻¹. ΔT_f = 1.86 × 6.91 = 12.9 K, so it freezes near −13 °C - short of the −15 °C requirement, and with no margin at all for a cold snap or for further dilution. As delivered it fails the specification for this fleet.
Reading the failure: the cracked radiator is the classic signature of dilution. Topping up with tap water lowers the glycol fraction, raises the freezing point, and water expands on freezing, splitting the core. Tap water also adds Ca²⁺/Mg²⁺, which scale the narrow tubes and reduce heat transfer, so the engine runs hotter and the coolant degrades faster.
Recommendation: buy concentrate, mix with distilled water to a measured freeze point slightly below the target, verify with a hydrometer at every service, and never top up with tap water. Note the tension in the brief: even the 35% ceiling corresponds to only about −16 °C, so the correct engineering answer is to relax the viscosity rule slightly rather than to run at exactly −15 °C.