Chemistry help for balancing equations and stoichiometry

alai is a notes app for iPad and the web with Ally, an adaptive AI tutor that teaches alongside you. A lot of chemistry homework is counting and converting, and one wrong number early on, like a changed subscript or the wrong mole ratio, carries through to the end.

Where chemistry goes wrong on paper

Balancing equations

A balanced equation has the same number of atoms of each element on both sides, and you get there by changing only the coefficients, the numbers in front of each formula. The subscripts are part of what each substance is, so changing one changes the substance (OpenStax Chemistry 2e, section 4.1).

• Changing a subscript. To balance H₂ + O₂ → H₂O, writing H₂ + O₂ → H₂O₂ makes the atoms match, but H₂O₂ is hydrogen peroxide. The balanced equation is 2H₂ + O₂ → 2H₂O.
• Stopping with an element still off. H₂ + O₂ → 2H₂O fixes the oxygen but leaves 4 hydrogen atoms on the right and only 2 on the left.
• Leaving the coefficients too big. 4H₂ + 2O₂ → 4H₂O is balanced, but every coefficient shares a factor of 2, so it reduces to 2H₂ + O₂ → 2H₂O.
• Not knowing where to start. For C₃H₈ + O₂ → CO₂ + H₂O, start with an element that appears in only one compound on each side. Carbon gives 3CO₂, hydrogen gives 4H₂O, and then the right side has 3(2) + 4(1) = 10 oxygen atoms, so you need 5O₂: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O.

Stoichiometry

Most stoichiometry problems follow the same path: grams of one substance to moles, moles of that substance to moles of the other using the coefficients of the balanced equation, then moles back to grams (OpenStax Chemistry 2e, section 4.3).

Take 2H₂ + O₂ → 2H₂O, with 4.0 g of H₂ and plenty of oxygen. H₂ has a molar mass of 2.0 g/mol, so 4.0 g is 2.0 mol. The coefficients of H₂ and H₂O are both 2, so 2.0 mol of H₂ makes 2.0 mol of H₂O. Water's molar mass is 18.0 g/mol, so that's 36 g of water.

• Using a ratio from the wrong pair. The ratio links the two substances you're converting between. Here that's H₂ and H₂O, so the 1 in front of O₂ doesn't belong in it.
• Skipping the moles. Coefficients count molecules and moles, so they can't be used as a ratio of grams.
• Picking the limiting reactant by the smaller number. In N₂ + 3H₂ → 2NH₃ with 3.0 mol of N₂ and 6.0 mol of H₂, the 3.0 mol of N₂ would need 9.0 mol of H₂. Only 6.0 mol is there, so H₂ runs out first and limits the reaction, even though there's more of it. It makes 4.0 mol of NH₃.

Significant figures

Measured numbers carry their precision through a calculation. OpenStax gives two rounding rules for calculations: when you multiply or divide, round to the fewest significant figures in the numbers you started with, and when you add or subtract, round to the fewest decimal places (OpenStax Chemistry 2e, section 1.5).

So 2.50 cm × 3.1 cm = 7.75 cm² rounds to 7.8 cm², because 3.1 has two significant figures. And 12.11 g + 0.3 g = 12.41 g rounds to 12.4 g, because 0.3 has one decimal place. Leading zeros, as in 0.0034, aren't significant. Zeros at the end of a number after the decimal point, as in 2.50, are. Counted and defined numbers, such as the coefficients in a balanced equation or the 100 in 1 m = 100 cm, don't limit the answer.

How Ally helps as you work

In Homework help, when you lift your pencil for about two seconds, or tap Check my work, Ally reads your newest line with the lines above it. If everything so far follows, Ally stays quiet. When a step goes wrong, Ally highlights the part that slipped and asks about it in one short sentence. The hint is meant to point at the slip and leave the coefficients, the conversions and the final answer to you.

Say you're balancing H₂ + O₂ → H₂O and you write H₂ + O₂ → H₂O₂. Ally highlights the H₂O₂ and asks a question like “Is H₂O₂ the same substance as H₂O?” You see that the formula changed, put it back to H₂O and balance with coefficients instead.

Or say you've found 2.0 mol of H₂ in the water problem above, and you hold the talk button to ask whether the ratio is 2 to 1 because of the O₂. Ally explains that oxygen is in excess, so it isn't part of this ratio, and asks a question like “What are the coefficients in front of H₂ and H₂O?”

A few more things that help in chemistry:

• Units are part of the answer. Ally treats a chemistry answer as finished only when it has a number and its units, such as 36 g.
• Ask why out loud. If you ask whether the limiting reactant is just the one you have less of, Ally explains that it depends on the mole ratio and asks how much of the other reactant you'd need.
• Molarity. If you ask about a molarity you got by dividing grams by milliliters, Ally reminds you that molarity is moles per liter and asks what the grams and milliliters need to become.
• Memory of past slips. If you've changed a subscript before, Ally can remind you what helped last time.

Common chemistry mistakes, one page each

• Balancing equations with subscripts: why only coefficients change
• Mole ratios: which coefficients go in the ratio
• Significant figures: how to round after multiplying, dividing, adding and subtracting

Comparing alai with other apps

For other ways to get help, see alai vs ChatGPT study mode and alai vs Khanmigo. For what the research says about hints that stop short of the answer, see homework help without answers.