Chemistry · applications · one sitting
Every box below is shut until you open it. Open one, ask the question out loud, let them guess, then reveal. The formulas are live: put real numbers in the fields and the page shows the whole chain, not just an answer.
Ten questions that get harder. It is not a test and nothing is graded — it tells you, in about eight minutes, which rung the room is actually standing on, so you know where today's lesson has to start.
Ball makes one decision early in the book that is worth stealing whole: every quantitative problem in chemistry is worked as one of two kinds, and never as a trick. His reason is the right one — a student who uses a shortcut and gets a wrong answer has no idea where it broke.
Objective
Given any problem in this course, name which of the two it is before writing a single number.You have a quantity. You want the same stuff expressed in a different unit. Multiply by fractions that equal 1, arranged so the unit you don't want cancels.
Read it aloud as: grams of chlorine, times one mole per 70.90 grams, gives moles. The grams cancel because one is upstairs and one is downstairs. That sentence is the method.
A relationship is already written down — PV = nRT, M = mol/L, pH = −log[H₃O⁺]. Identify the unknown, rearrange, substitute with units attached.
The road map
Almost every reaction problem is the same three moves, and the middle one is the only place the balanced equation is allowed in:| # | Check | What goes wrong without it |
|---|---|---|
| 1 | Is the equation balanced? | Your mole ratio is fiction. |
| 2 | Did you convert to moles before the arrow? | You multiplied grams by a mole ratio. Nothing means anything after that. |
| 3 | Do the units cancel to what you were asked for? | You have a number with the wrong unit, which is a wrong answer. |
| 4 | Sig figs — how precise was the worst measurement? | You report six digits of confidence you never had. |
Eight applications. Each box holds the situation, the formula, a worked example, a faded one where they finish the last step themselves, and a live solver. Work them in order or pull the one you need.
Objective
From a chemical formula, calculate the mass of one mole of it.Add up the atomic mass of every atom in the formula. A subscript multiplies what it follows; a subscript after a parenthesis multiplies everything inside it.
The trap: the 2 outside the bracket multiplies both the N and the three O's. Six oxygens, not three.
Test yourself — what is the molar mass of (NH₄)₂SO₄, ammonium sulfate? Fertilizer. Answer in g/mol.
Solver · molar mass
Write subscripts as ordinary numbers: H2O, Ca(NO3)2, Al2(SO4)3. Hydrate dots (·5H2O) are not parsed — add the water by hand.
Key takeaway
Molar mass is a conversion factor with two faces: g/mol going one way, mol/g going the other. Which face you use is decided entirely by which unit you need to cancel.Objective
Move in any direction between grams, moles, and number of particles.Faded example — finish the last step. You have 2.00 mol of water. How many molecules is that?
Solver · mass ↔ moles ↔ particles
Fill mass or moles, not both — whichever you leave blank is what gets calculated.
Key takeaway
The mole is a count, like a dozen. Everything else in this lesson is that one idea wearing different clothes.Objective
From a given mass of one substance, calculate the mass of another substance in the same reaction.Worked, in one line — 86.4 g of potassium into MgCl₂ + 2K → Mg + 2KCl:
Three fractions, three cancellations, one surviving unit. The middle fraction is the only one that came from the balanced equation.
Test yourself — what mass of H₂ is produced when 122 g of Zn react? Zn + 2HCl → ZnCl₂ + H₂
Solver · mass A → mass B
Loaded with the airbag: 130 g of NaN₃ in 2NaN₃ → 2Na + 3N₂.
Key takeaway
You may never take a mole ratio across grams. Convert, cross, convert back — in that order, every time.Objective
Given amounts of two reactants, decide which one limits the reaction, and calculate how much product it can make.The method: convert both to moles, divide each by its own coefficient, and the smaller answer is the one that runs out.
Predict before you calculate — you double the hydrogen to 24.0 g and leave the nitrogen at 35.0 g. Does the yield of ammonia go up?
Solver · limiting reagent & theoretical yield
Key takeaway
Divide moles by coefficient. The smallest quotient names the limiting reagent — and that reagent alone sets the yield.Objective
Calculate percent yield, and say which of the two numbers in it came from a balance and which came from a calculation.Theoretical yield is the answer from box C or D. Actual yield can only come from weighing the thing you made. A percent yield over 100 does not mean you beat chemistry — it means your product is still wet.
Test yourself — the theoretical yield of ammonia was 42.6 g. You collect 31.0 g. What is the percent yield?
Solver · percent yield
Key takeaway
Theoretical yield is what the equation permits. Actual yield is what the balance says. The ratio is a statement about technique, not about chemistry.Objective
Calculate molarity from mass and volume, and dilute a stock solution to a working concentration.The dilution formula is a conservation statement in disguise: adding water changes the volume and the concentration, but not the number of moles already in the flask.
Test yourself — you need 500. mL of 0.100 M HCl and you have 2.00 M stock. What volume of stock do you measure out?
Solver · molarity
Solver · dilution (M₁V₁ = M₂V₂)
Key takeaway
Dilution moves volume and concentration in opposite directions and leaves the moles alone. That is the whole formula.Objective
Solve PV = nRT for any one of the four quantities, and connect it back to the mole answer from box C.Closing the loop on the airbag: box C says 130 g of NaN₃ gives 3.00 mol of N₂. At 25 °C and 1.00 atm that is V = nRT/P = (3.00)(0.08206)(298.15)/1.00 ≈ 73 L — the right order of magnitude for a driver's airbag, which is the point of the whole design.
Predict — a sealed rigid canister is heated from 25 °C to 50 °C. Does the pressure inside double?
Solver · PV = nRT
Enter temperature in °C — the solver converts to kelvin and shows it doing so.
Key takeaway
Four quantities, one equation, and a unit rule that is not negotiable: kelvin, litres, atmospheres, moles.Objective
Convert between hydronium concentration and pH, and say what one pH unit is actually worth.One pH unit is a factor of ten. Lemon juice at pH 2 is not "twice" as acidic as tomato juice at pH 4 — it is a hundred times.
Test yourself — a solution has [H₃O⁺] = 1.0 × 10⁻⁵ M. What is its pH?
Solver · pH ↔ [H₃O⁺]
Key takeaway
pH is a compressed scale. Every step of 1 is a tenfold change in the thing that actually does the chemistry.Saved in this browser as you type. They stay on this machine — nothing is sent anywhere.
What the ramp revealed — where the room actually is
What landed, what didn't
For next time
Backward fading. Each application gives a complete worked example first, then a problem where only the last step is left to the student, then an open problem. In a study of 47 underprepared college chemistry students, 74 % preferred faded examples to open-ended problems, and that cohort finished the semester ahead of their college-ready peers on both multiple-choice and open-ended final questions. A blank problem is not harder teaching; it is less teaching.
Prediction before reveal. Two boxes here ask for a prediction that most rooms get wrong — the excess-reactant question in D and the Celsius-doubling question in G. Being wrong out loud first is what makes the correction stick. Neither is scored.
Answers one action away, never hidden. Every check reveals the reasoning, not just a verdict, because a student who cannot see where the logic broke learns nothing from being told they are wrong.
Collapsed by default. Only one thing is open at a time so the screen never becomes a wall. You control what the room sees.
Two problem types, no shortcuts. Taken from the book: consistency in problem solving beats clever tricks, because tricks fail silently.
Sources: Ball, Introductory Chemistry — ch. 5 (stoichiometry and the mole), ch. 6 (gases), ch. 11 (solutions), ch. 12 (acids and bases). Faded-example findings: Exploring the Use of Faded Worked Examples as a Problem Solving Approach for Underprepared Students, ERIC EJ1086007.
The Working Bench · built for one sitting · all solver math verified against the book's own worked answers