The factor-label method

53 written problems across two levels — 35 foundational · 18 advanced. Work through them on paper, then reveal every answer to check. These are not graded and are counted separately from adaptive practice.

Foundational

1. FoundationalWhat is a conversion factor?

2. FoundationalWrite the two conversion factors from " $1\ \text{h} = 60\ \text{min}$ ".

3. FoundationalConvert $3480\ \text{s}$ to minutes.

4. FoundationalConvert $2.5\ \text{h}$ to seconds.

5. FoundationalA car travels $80\ \text{km}$ in $1\ \text{h}$ . How far in $8.5\ \text{h}$ ?

6. FoundationalEggs cost $\$1.44/\text{doz}$ . What do $2\ \text{doz}$ cost?

7. FoundationalHow many individual eggs can $\$4.32$ buy if eggs are $\$1.44/\text{doz}$ and $12\ \text{eggs/doz}$ ?

8. FoundationalIn "What is the cost of $2\ \text{doz}$ eggs if eggs are $\$1.44/\text{doz}$ ?", name the initial amount.

9. FoundationalIn the same problem, what is the conversion statement?

10. FoundationalA chemical costs $\$50/\text{g}$ . What is the cost of $100\ \text{g}$ ?

11. FoundationalCork has a density of $0.35\ \text{g/mL}$ . What is the volume of $20\ \text{g}$ of cork?

12. FoundationalOne mole of oxygen has a mass of $32\ \text{g}$ . What is the mass of $5.5\ \text{mol}$ ?

13. FoundationalIf $3$ kiwi fruit sell for $\$1$ , how many can you buy for $\$5$ ?

14. FoundationalA gas tank holds $39.5\ \text{L}$ . If $1\ \text{L} = 0.264\ \text{gal}$ and gas is $\$1.26/\text{gal}$ , what does a fill cost?

15. FoundationalHow do you know instantly that $5.00\ \text{mL} \times \dfrac{0.200\ \text{mL}}{3.86\ \text{g}}$ is set up wrong to find a mass?

16. FoundationalWhich way up must the factor be written to convert a mass in grams to a volume in mL using a density?

17. FoundationalA reaction is complete in $5.0 \times 10^{-4}\ \text{s}$ . If $1\ \text{ms} = 10^{-3}\ \text{s}$ , how many ms is that?

18. FoundationalIf $1\ \text{mol}$ of a gas has a volume of $22.4\ \text{L}$ , how many moles are in $25.0\ \text{L}$ ?

19. FoundationalA current of $35\ \text{coulombs/s}$ flows. How long to deliver $200\ \text{coulombs}$ ?

20. FoundationalConcentrated HCl is $11.7\ \text{mol/L}$ . What volume contains $0.0358\ \text{mol}$ ?

21. FoundationalSugar costs $\$0.980/\text{kg}$ and $1\ \text{t} = 1000\ \text{kg}$ . How many tonnes can $\$350$ buy?

22. FoundationalWhy must you ALWAYS include units in a conversion?

23. FoundationalA car travels at $120\ \text{km/h}$ . How far in $0.25\ \text{h}$ ?

24. FoundationalThe same car ( $120\ \text{km/h}$ ): how far in $12\ \text{min}$ ?

25. FoundationalBeakers cost $\$8.40/\text{doz}$ . Harry breaks $3\ \text{doz}$ . What does he owe?

26. FoundationalIf $1\ \text{yard} = 3\ \text{feet}$ , $1\ \text{foot} = 12\ \text{inches}$ and $1\ \text{cm} = 0.3937\ \text{inch}$ , how many cm in $5\ \text{yards}$ ?

27. FoundationalConvert $250\ \text{g}$ of a $5\%$ -by-mass salt solution: how many grams of salt does it contain?

28. FoundationalWater contains $8\ \text{ppm}$ of dissolved oxygen. Write the equivalence this represents.

29. FoundationalWhat is the name of the general method of multiplying by conversion factors so units cancel?

30. FoundationalIf your setup leaves the unit $\text{mL}^2/\text{g}$ but the question asked for grams, what does that tell you?

31. FoundationalA rate of $120\ \text{km/h}$ is a conversion factor between which two quantities?

32. FoundationalAn ore is $3\%$ copper by mass. How much copper is in $500\ \text{g}$ of ore?

33. FoundationalIs the factor $\dfrac{1000\ \text{g}}{1\ \text{kg}}$ exact or measured, and does it limit significant figures?

34. FoundationalRoughly, should converting $3480$ seconds to minutes give a bigger or smaller number, and why?

35. FoundationalWhy is learning conversion factors so important for the rest of the chemistry course?

Advanced

36. AdvancedConvert $2\ \text{m}^3$ to $\text{cm}^3$ .

37. AdvancedConvert a speed of $90\ \text{km/h}$ to metres per second.

38. AdvancedAn area of $2.5\ \text{m}^2$ is to be expressed in $\text{cm}^2$ . Give the value and explain the common error.

39. AdvancedA $2.0\ \text{L}$ solution is $1.5\ \text{mol/L}$ in acid. How many moles of acid are present?

40. AdvancedGold is $19.3\ \text{g/mL}$ . Using it as a conversion factor, find the mass of $0.500\ \text{mL}$ of gold.

41. AdvancedConvert $2.50\ \text{h}$ to seconds and state the correct number of significant figures with reasoning.

42. AdvancedA $250\ \text{mL}$ vinegar sample is $5.0\%$ acetic acid by mass and has a density of $1.01\ \text{g/mL}$ . Find the mass of acetic acid.

43. AdvancedCopper ore is $0.80\%$ copper. What mass of ore is needed to obtain $40\ \text{kg}$ of copper?

44. AdvancedAir pollution is measured at $350\ \text{ppm}$ of a gas. How many grams of the gas are in $2.0\ \text{kg}$ of air?

45. AdvancedExplain why a magnitude sanity check would catch converting $2.5\ \text{h}$ to seconds and getting $0.000694$ .

46. AdvancedA rectangular tank is $2.0\ \text{m}$ by $1.5\ \text{m}$ by $0.50\ \text{m}$ . Find its volume in litres. ( $1\ \text{m}^3 = 1000\ \text{L}$ )

47. AdvancedA car uses fuel at $8.0\ \text{L}/100\ \text{km}$ . How many litres for a $250\ \text{km}$ trip?

48. AdvancedSeawater is about $3.5\%$ dissolved salts by mass. What mass of salts is in $1.0\ \text{kg}$ of seawater?

49. AdvancedWhy can converting $1\ \text{cm}^3$ to $\text{mm}^3$ never be done by multiplying by $10$ only once?

50. AdvancedA gold chain has a volume of $0.50\ \text{cm}^3$ . Gold is $19.3\ \text{g/cm}^3$ and costs $\$60/\text{g}$ . What is the chain’s gold worth?

51. AdvancedA $0.250\ \text{L}$ sample of blood contains glucose at $1.0\ \text{g/L}$ . Express the glucose mass, and say which factors are exact vs measured.

52. AdvancedConvert 2.5 km to centimetres.

53. AdvancedHow many seconds are there in 3.0 days?