Worked solutions for example 2 Workshop 1 - Units and Conversions OES Contextual problems

1. 2a How many grams are there in 3 moles of H2O?

2. 2a • Calculate how many grams are in one mole by multiplying
the number of atoms of each element by their mass:

3. 2a • Calculate how many grams are in one mole by multiplying
the number of atoms of each element by their mass:
1 mole = 2 x 1.0079 + 1 x 15.999 = 18.015g

4. 2a • Calculate how many grams are in one mole by multiplying
the number of atoms of each element by their mass:
1 mole = 2 x 1.0079 + 1 x 15.999 = 18.015g
• Multiply this by the number of moles in the sample:

5. 2a • Calculate how many grams are in one mole by multiplying
the number of atoms of each element by their mass:
1 mole = 2 x 1.0079 + 1 x 15.999 = 18.015g
• Multiply this by the number of moles in the sample:
3 x 18.015 = ퟓퟒ. ퟎퟒퟒퟒ퐠

6. 2b Calculate the number of moles of calcium in a 1kg rock
sample, if the rock is 411 ppm calcium.

7. 2b • Convert ppm to g per kg:

8. 2b • Convert ppm to g per kg:
441ppm = 441μg per g

9. 2b • Convert ppm to g per kg:
441ppm = 441μg per g
441,000μg per kg = 0.441g per kg

10. 2b • Convert ppm to g per kg:
441ppm = 441μg per g
441,000μg per kg = 0.441g per kg
• Divide by the mass of one mole of calcium:

11. 2b • Convert ppm to g per kg:
441ppm = 441μg per g
441,000μg per kg = 0.441g per kg
• Divide by the mass of one mole of calcium:
1 mole Ca = 40.078g

12. 2b • Convert ppm to g per kg:
441ppm = 441μg per g
441,000μg per kg = 0.441g per kg
• Divide by the mass of one mole of calcium:
1 mole Ca = 40.078g
0.441
40.078
= ퟎ. ퟎퟏퟐ퐦퐨퐥 퐂퐚

13. 2c Seawater contains around 10.8 ppt (parts per
thousand) sodium. What is this in mol/kg Na?

14. 2c • Convert ppt to g per kg:

15. 2c • Convert ppt to g per kg:
10.8ppt = 10.8g per kg

16. 2c • Convert ppt to g per kg:
10.8ppt = 10.8g per kg
• Divide by the mass of sodium:

17. 2c • Convert ppt to g per kg:
10.8ppt = 10.8g per kg
• Divide by the mass of sodium:
1 mole Na = 22.99g

18. 2c • Convert ppt to g per kg:
10.8ppt = 10.8g per kg
• Divide by the mass of sodium:
1 mole Na = 22.99g
10.8
22.99
= ퟎ. ퟒퟕ퐦퐨퐥퐤퐠−ퟏ 퐍퐚

19. 2d If all river water contained 45 ppb PO43-, and flowed
into the ocean at 3.6 x 1016 kg/year, what would be
the flux of PO43- into the ocean in mol/yr? (Hint: First
convert PO43- from ppb to molkg-1.)

20. 2d • Convert from ppb to moles per kg:

21. 2d • Convert from ppb to moles per kg:
45ppb = 45ng per g = 45μg per kg

22. 2d • Convert from ppb to moles per kg:
45ppb = 45ng per g = 45μg per kg
1 mole PO4 3
− = 30.974 + 4 15.999 = 94.97g

23. 2d • Convert from ppb to moles per kg:
45ppb = 45ng per g = 45μg per kg
1 mole PO4 3
− = 30.974 + 4 15.999 = 94.97g
45 x 10−6gkg−1
94.97g
= 4.74 x 10−7molkg−1

24. 2d • Convert from ppb to moles per kg:
45ppb = 45ng per g = 45μg per kg
1 mole PO4 3
− = 30.974 + 4 15.999 = 94.97g
45 x 10−6gkg−1
94.97g
= 4.74 x 10−7molkg−1
• Multiply by the flux of water:

25. 2d • Convert from ppb to moles per kg:
45ppb = 45ng per g = 45μg per kg
1 mole PO4 3
− = 30.974 + 4 15.999 = 94.97g
45 x 10−6gkg−1
94.97g
= 4.74 x 10−7molkg−1
• Multiply by the flux of water:
4.74 x 10−7molkg−1 x 3.6 x 1016kgyr−1 = ퟏ. ퟕퟏ 퐱 ퟏퟎퟏퟎ퐦퐨퐥퐲퐫−ퟏ 퐏퐎ퟒퟑ−