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Lesson 13 · Estimate, then compute
One digit first
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One digit first

Before any calculator, run the one-digit version: round every value to a single digit, multiply or divide in your head, and count the zeros. 3.93.9 of 5.25.2 grams? Call it 4 of 5 — about three-quarters. 4 mol4\ \mathrm{mol} at 300 kJ/mol300\ \mathrm{kJ/mol}? Four threes and two zeros — a thousand-ish kJ. Five seconds, no buttons.

Here is why it pays: a slipped decimal SURVIVES a calculator — the screen shows confident garbage, ten times too big, and nothing on it blushes. It never survives an estimate, because a wrong power of ten stands a full 10× from your anchor. Estimate first, compute second, and let the two shake hands before you write anything down. Professional scientists never stop doing this; they just stop admitting it.

mtheoreticalmactual% yield

% yield=mactualmtheoretical×100%\%\,\text{yield} = \frac{m_{\text{actual}}}{m_{\text{theoretical}}} \times 100\%

  • % yield\%\,\text{yield}= Percent yield (concentration)
  • mactualm_{\text{actual}}= Actual yield (mass obtained) (mass)
  • mtheoreticalm_{\text{theoretical}}= Theoretical yield (mass predicted) (mass)
Percent Yield solver →
qΔHn

q=nΔHq = n \Delta H

  • qq= Heat released or absorbed (energy)
  • nn= Amount of substance (amount of substance)
  • ΔH\Delta H= Molar enthalpy change (molar energy)
Heat of Reaction solver →