Worked solutions for example 4 Workshop 1 - Units and Conversions OES Contextual problems

1. 4a 1ml of water occupies a volume of 1cm3. How many
litres will 5cm3 of water occupy?

2. 4a • Convert 1ml into litres:

3. 4a • Convert 1ml into litres:
1ml = 0.001L

4. 4a • Convert 1ml into litres:
1ml = 0.001L
• Multiply this by the size of the sample:

5. 4a • Convert 1ml into litres:
1ml = 0.001L
• Multiply this by the size of the sample:
5cm3 = 5ml = 0.001L x 5 = ퟓ 퐱 ퟏퟎ−ퟑ퐋

6. 4b There are 1.4 x 1021L of water in the ocean. What is
this in cubic metres?

7. 4b • Work out the conversion between cm3 and m3:

8. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m

9. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3

10. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:

11. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:
1ml = 1cm3

12. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:
1ml = 1cm3
1 x 10−3L = 1 x 10−6m3

13. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:
1ml = 1cm3
1 x 10−3L = 1 x 10−6m3
1L = 1 x 10−3m3

14. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:
1ml = 1cm3
1 x 10−3L = 1 x 10−6m3
1L = 1 x 10−3m3
• Multiply by the volume of the ocean:

15. 4b • Work out the conversion between cm3 and m3:
1cm = 0.01m
1cm3 = cm x cm x cm = 0.01 x 0.01 x 0.01 m3 = 1 x 10−6m3
• Work out the conversion between 1L and 1m3:
1ml = 1cm3
1 x 10−3L = 1 x 10−6m3
1L = 1 x 10−3m3
• Multiply by the volume of the ocean:
1.4 x 1021L = 1.4 x 1021 x 10−3 m3 = ퟏ. ퟒ 퐱 ퟏퟎퟏퟖ퐦ퟑ

16. 4c Seawater contains about 142mgL-1of bicarbonate.
How many grams of bicarbonate will there be in a 2m3
sample of seawater?

17. 4c • Convert 142 mgL-1 into 142 mgm-3:

18. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3

19. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3

20. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3
1퐿−1 = 103푚−3

21. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3
1퐿−1 = 103푚−3
142푚푔퐿−1 = 142 푥 103푚푔푚−3 = 1.42 푥 105푚푔푚−3

22. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3
1퐿−1 = 103푚−3
142푚푔퐿−1 = 142 푥 103푚푔푚−3 = 1.42 푥 105푚푔푚−3
• Multiply by the sample size and convert mg to g:

23. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3
1퐿−1 = 103푚−3
142푚푔퐿−1 = 142 푥 103푚푔푚−3 = 1.42 푥 105푚푔푚−3
• Multiply by the sample size and convert mg to g:
1.42 푥 105푚푔푚−3 푥 2푚3 = 2.84 푥 105푚푔

24. 4c • Convert 142 mgL-1 into 142 mgm-3:
1퐿 = 1 푥 10−3푚3
1
1
퐿−1 =
1
10−3 푚−3
1퐿−1 = 103푚−3
142푚푔퐿−1 = 142 푥 103푚푔푚−3 = 1.42 푥 105푚푔푚−3
• Multiply by the sample size and convert mg to g:
1.42 푥 105푚푔푚−3 푥 2푚3 = 2.84 푥 105푚푔
2.84 푥 105 푥 10−3 = ퟐퟖퟒ품

25. 4d There is approximately 1.81 x 1021g of magnesium in
the entire ocean. For any sample of seawater,
calculate the magnesium content in molL-1.

26. 4d • Calculate the number of moles of Mg in the ocean:

27. 4d • Calculate the number of moles of Mg in the ocean:
1 mole Mg = 24.305g

28. 4d • Calculate the number of moles of Mg in the ocean:
1 mole Mg = 24.305g
1.81 x 1021
24.305
= 7.45 x 1019mol Mg

29. 4d • Calculate the number of moles of Mg in the ocean:
1 mole Mg = 24.305g
1.81 x 1021
24.305
= 7.45 x 1019mol Mg
• Use the volume of the ocean to work out the overall
concentration of Mg in seawater:

30. 4d • Calculate the number of moles of Mg in the ocean:
1 mole Mg = 24.305g
1.81 x 1021
24.305
= 7.45 x 1019mol Mg
• Use the volume of the ocean to work out the overall
concentration of Mg in seawater:
7.45 x 1019mol Mg
1.4 x 1021L
= ퟎ. ퟎퟓퟑ퐦퐨퐥퐋−ퟏ