Why can't I use the mole ratio on grams?
Updated
The short answer
The coefficients in a balanced equation compare numbers of molecules, and each substance has its own molar mass, so the ratio holds for moles and breaks for grams. Convert grams to moles first, use the mole ratio, then convert back to grams if the question asks for a mass.
What it looks like
How many grams of O₂ react with 4.00 g of H₂? The equation is 2H₂ + O₂ → 2H₂O. Use H₂ = 2.016 g/mol and O₂ = 32.00 g/mol.
| Step | Wrong | Right |
|---|---|---|
| Grams to moles | skipped | 4.00 g H₂ ÷ 2.016 g/mol = 1.984 mol H₂ |
| Mole ratio | 4.00 g H₂ × (1 g O₂ / 2 g H₂) = 2.00 g O₂ | 1.984 mol H₂ × (1 mol O₂ / 2 mol H₂) = 0.9921 mol O₂ |
| Moles to grams | skipped | 0.9921 mol O₂ × 32.00 g/mol = 31.7 g O₂ |
The equation says one O₂ molecule reacts for every two H₂ molecules. An O₂ molecule is about 16 times heavier than an H₂ molecule, so the wrong answer comes out about 16 times too small.
In alai, an iPad app that reads your handwriting as you work, Ally, the tutor, would point at the 1 g O₂ / 2 g H₂ factor and ask about its units.
Why it happens
The coefficients look like they apply to whatever amount is in front of you. In a lab problem that's usually grams, because grams are what a balance measures.
Moles and grams also both feel like “how much,” so it's natural to read 2H₂ + O₂ as two parts hydrogen to one part oxygen by weight. The equation counts particles. One mole of H₂ is about 2 g and one mole of O₂ is about 32 g, so equal numbers of molecules have very different masses.
OpenStax Chemistry 2e calls the ratios from the coefficients stoichiometric factors, and every calculation in its stoichiometry section uses one. The same factor can also land upside down, as 2 mol H₂ / 1 mol O₂ when you need the reverse. Writing the substance next to every unit catches that slip too.
How to catch it yourself
Write the unit and the substance on every number, like 1.984 mol H₂, then ask:
What unit belongs on the numbers you took from the balanced equation?
Try these
Use H₂ = 2.016 g/mol, O₂ = 32.00 g/mol, H₂O = 18.02 g/mol and CH₄ = 16.04 g/mol.
- N₂ + 3H₂ → 2NH₃. How many moles of NH₃ form from 6.0 mol of H₂?
- 2H₂ + O₂ → 2H₂O. How many grams of water can 8.00 g of O₂ make with plenty of H₂?
- CH₄ + 2O₂ → CO₂ + 2H₂O. How many grams of O₂ does it take to burn 16.0 g of CH₄?
Answers
- 6.0 mol H₂ × (2 mol NH₃ / 3 mol H₂) = 4.0 mol NH₃
- 8.00 g ÷ 32.00 g/mol = 0.250 mol O₂, then × (2 mol H₂O / 1 mol O₂) = 0.500 mol H₂O, then × 18.02 g/mol = 9.01 g H₂O
- 16.0 g ÷ 16.04 g/mol = 0.9975 mol CH₄, then × (2 mol O₂ / 1 mol CH₄) = 1.995 mol O₂, then × 32.00 g/mol = 63.8 g O₂. Putting the 2 straight onto grams would give 32.0 g, about half the real amount.
How alai helps
alai is a notes app for iPad and the web. In Homework help, its tutor, Ally, follows each line of a calculation as you write it, and if a ratio from the equation lands on grams, Ally points at that factor and asks a question about it. If you want to hear why the coefficients count molecules, you can hold to talk and ask Ally.