Gym

Endless generated quantity-algebra where the units do the bookkeeping. Convert between volume, molarity, moles, and mass — one conversion factor at a time — and watch the units cancel down the chain. Type your answer: every value is machine-computed, and if your entry matches a known cancellation mistake it is named, not just marked wrong.

Name an ionic compound from its formula, and write the formula from the name — both directions, including the Stock system (iron(III), copper(I)) for variable-charge metals. The formula is assembled by machine-verified charge crossover; every wrong option is a specific naming mistake (wrong oxidation state, charges used as subscripts, or covalent prefixes on an ionic compound).

The periodic table is a database with patterns, and the patterns have exceptions. These drills ask you to compare sourced values — covalent radius, first ionization energy, electronegativity — across periods and down groups, to predict common ions from group position, and to order elements by ionization energy. Every answer is checked against the curated data behind the Valence Table; when the data breaks the naive rule, the explanation names the exception instead of pretending the rule is a law.

Pick the balanced equation — then watch every element tally to equal counts on both sides. ChemKernel balances each reaction as the one integer solution of the conservation matrix, so the answer is derived, not guessed. Wrong options are named mistakes: a coefficient that leaves an element unbalanced, or the classic trap of changing a subscript (which silently swaps in a different substance). Coefficients balance the equation; subscripts define the compound and never change.

Chemists sort reactions by their pattern — and the pattern tells you what to expect. These drills give you a balanced equation and ask which family it belongs to (combustion, synthesis, decomposition, single or double replacement, precipitation, acid-base neutralization, or gas evolution), or which ions are spectators that sit out the reaction. Every equation is balanced and classified by the engine, and the explanations show the evidence — a free element changing hands, an insoluble solid dropping out, an acid meeting a base.

Convert a mass of one species to a mass of another across a balanced equation: grams → moles → (cross the mole ratio) → moles → grams. The equation is balanced by ChemKernel, the molar masses are sourced, and every value is exact. Type the mass you get — enter a known mistake (the mole ratio flipped, ignored, or the grams→moles step skipped) and it is named for you, not offered as a giveaway to eliminate.

Two reactants are mixed by mass — which one limits the reaction, and how much product can form? Convert each mass to moles, divide by its coefficient to get the reaction extent it can reach, and the smaller one wins: it runs out first and sets the theoretical yield. Every value is exact and machine-verified. Type the maximum product mass — sizing it from the reagent that is actually in excess is the classic mistake, named when you enter it.

Given how much reactant went in and how much product actually came out, find the percent yield: work out the theoretical yield by mass stoichiometry, then take actual ÷ theoretical × 100. The theoretical yield is machine-computed from a sourced, balanced equation. Type the percent — a common wrong answer (the ratio inverted, the ×100 dropped, or the reactant mass used as the denominator) is named when you enter it, never handed to you as an option to rule out.

The ideal gas law ties a gas's pressure, volume, amount, and temperature into one equation. These drills give you three of the four and ask for the fourth — and a second set walks a fixed sample from one state to another with the combined gas law. Type your answer (rounded to three significant figures); if you slip, the drill names the mistake — most often forgetting to convert °C to kelvin, or reaching for R = 8.314 when a pressure-in-atm problem wants R = 0.08206. The arithmetic is machine-checked; the ideal-gas model is disclosed, not proved.

Heat, mass, specific heat, temperature change — one equation ties them together: q = m·c·ΔT. These drills give you three and ask for the fourth, drawing each substance's specific heat from a sourced table (water 4.184, aluminum 0.897, and metals down to gold's 0.129 J/g·°C). Type your answer (rounded to three significant figures); if you slip, the drill names the mistake — most often treating every substance like water, or dropping a factor. The arithmetic is machine-checked; the specific heats are sourced and the calorimetry model is disclosed, not proved.

A Lewis structure is an electron ledger: count the valence electrons, spread them into bonds and lone pairs, and the shape follows. These drills give you a molecule and ask for its valence-electron total, the number of electron domains around the central atom, or its molecular shape. Type the counts (they are exact — this is integer accounting, machine-checked); if you slip, the drill names the mistake — counting every electron instead of just the valence ones, forgetting a lone pair is a domain, or calling a double bond two domains. The shape questions offer the electron-domain geometry as a tempting wrong answer: lone pairs are invisible in the named shape.

A weak acid only partly ionizes, so its pH is not simply −log of its concentration — you have to solve the equilibrium. Each drill gives a weak acid, its Kₐ, and how concentrated the solution is; you find the pH the real way, from the ICE table's mass-action root (the same solver the acetic-acid lesson uses). Type your answer (rounded to three significant figures). If you slip, the drill names the mistake — treating the weak acid as strong (pH = −log[HA]₀), confusing Kₐ with the hydrogen-ion concentration (that gives the pKₐ), or forgetting the square root in [H⁺] = √(Kₐ·[HA]₀). The arithmetic is machine-checked; the equilibrium model is disclosed, not proved, and Kₐ is a sourced measured value.

A reaction's ORDER sets its clock. Each drill gives a reaction, its measured order, and its rate constant k (a sourced value), and asks one of three things: how much reactant is left after a time t (apply the order's integrated rate law — [A]₀−kt for zero order, [A]₀e^(−kt) for first, 1/[A]₀+kt for second), what its half-life is (t½ = [A]₀/2k, ln2/k, or 1/k[A]₀), or — given three successive half-lives — what the order must be. Type the numeric answers to three significant figures; pick the order from the menu. The one mistake the drill keeps catching is using the WRONG order's formula, so every diagnostic names which order you slipped into. The arithmetic is machine-checked; the rate law and order are a disclosed model, and k is a sourced measured value.