Chemistry · Rung 9 of 24

Solutions and gases

Almost all chemistry happens in solution or in the gas phase, so both need measuring. Molar concentration is moles of solute per litre of solution, not of solvent, and diluting conserves the amount of solute: C₁V₁ = C₂V₂. For gases, the law that subsumes the rest is PV = nRT, with R = 0.082 atm·L/(mol·K), and the temperature always in kelvin, because in Celsius doubling the temperature doubles nothing. It follows that one mole of any gas occupies 22.4 litres at 0 °C and one atmosphere. And changes of state are read off the phase diagram: the triple point is where all three coexist, and if that point sits above one atmosphere, the solid never melts at ambient pressure — it sublimes. That happens to CO₂, which is why dry ice is called dry.

Where this sits

Comes after
The mole and the sums
Opens up
Acids and bases, Air, water and soil

Exercises from this rung

Generated by the app, from easiest to hardest

  1. You take 100 mL of a 2 M solution and add water up to 400 mL. What concentration is left?

    • 0.5 M
    • 8 M
    • 2 M
    • 1 M

    Why Diluting adds and removes no solute: the amount is conserved and only the volume changes, so C₁V₁ = C₂V₂. Here 2 × 100 = C₂ × 400, giving C₂ = 0.5 M. The mental shortcut is that you multiplied the volume by four, so the concentration divides by four. And always add acid to water, never the other way round.

    easier

  2. You double a gas's pressure at constant temperature. What happens to the volume?

    • It halves
    • It drops to a quarter
    • It doubles
    • It does not change

    Why This is Boyle's law, which falls out of PV = nRT with n and T fixed: if the product PV is constant, doubling one halves the other. It is what you feel capping a syringe with your finger and pushing the plunger, and also what makes surfacing too fast from a dive dangerous: the air in the lungs expands as the pressure drops.

    in between

  3. Why does dry ice not get things wet?

    • Because it goes from solid to gas without being liquid
    • Because it repels water
    • Because it is colder than ordinary ice
    • Because the liquid evaporates at once

    Why CO₂'s triple point sits at 5.1 atmospheres, well above street pressure. Below that pressure the liquid does not exist, so on warming the solid goes straight to gas: it sublimes. Hence “dry”, and hence the fog on stage. With enough pressure CO₂ is a liquid, and that is how it sits inside a fire extinguisher.

    harder