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anonymous

  • one year ago

A solid substance has a density of 12 g/mL. A cube made out of this substance has 1 mm edge length. If the atomic mass of the substance is 120.0 g/mol, calculate how many moles of the substance are in this cube.

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  1. aaronq
    • one year ago
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    first find the volume of the cube, then find the mass with the density, finally convert the mass to moles

  2. anonymous
    • one year ago
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    How do you find the volume?

  3. aaronq
    • one year ago
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    |dw:1442365426768:dw|

  4. anonymous
    • one year ago
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    So do you find the mass by using the density formula?

  5. aaronq
    • one year ago
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    yep

  6. aaronq
    • one year ago
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    you'll have to convert the volume (or the density) to match the units

  7. anonymous
    • one year ago
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    I'm trying to work it out and getting confused.

  8. Jhannybean
    • one year ago
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    \[\sf \rho = \frac{m}{v} \\ \rho = 120~\frac{g}{mL}~,~~v =(1mm)^3 \] \[\sf 1~mm^3 ~\times~ \left(\frac{1~cm}{1~mm}\right)^3~\times~\frac{1~mL}{1~cm^3} =~1~mL\] \[\sf \frac{120~g}{mL} =\frac{m}{1~mL}~\implies m = 120~g\]

  9. Jhannybean
    • one year ago
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    When I see a value or conversion factor, I typically try to associate it with an appropriate formula

  10. aaronq
    • one year ago
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    you made a mistake, 1 cm = 10 mm, so: \(\sf \large 1~mm^3 ~\times~ \left(\frac{1~cm}{10~mm}\right)^3~\times~\frac{1~mL}{1000~cm^3} =~0.001~mL\)

  11. Jhannybean
    • one year ago
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    ...it was a typo <_<

  12. aaronq
    • one year ago
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    suuuuure it was :P

  13. aaronq
    • one year ago
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    A+ for effort

  14. anonymous
    • one year ago
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    Um...which way is it?

  15. Jhannybean
    • one year ago
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    The way @aaronq wrote.

  16. anonymous
    • one year ago
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    Thanks

  17. anonymous
    • one year ago
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    Would it be 1000 or 100 for cm^3?

  18. anonymous
    • one year ago
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    Alright. I was wondering why there was an extra 0

  19. anonymous
    • one year ago
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    Thanks for the help!

  20. Jhannybean
    • one year ago
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    Ok that was my fault. I had it backwards. \[\sf 1~mm^3 \times\left(\frac{1~cm}{10~mm}\right)^3~\times~ \frac{1~mL}{1~cm^3} =~1.0~\times~10^{-3}~mL \]Thats what it should be. There should be no 1000.

  21. Jhannybean
    • one year ago
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    So once we have this, create a ratio: \[\sf \frac{120~g}{1~mL} = \frac{m}{1.0~\times~10^{-3}~mL} \implies m=~(120 \cdot 1.0~\times~10^{-3})g\]

  22. aaronq
    • one year ago
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    i made a mistake too..it's supposed to be: \(\sf \large 1~mm^3 ~\times~ \left(\frac{1~cm}{10~mm}\right)^3~\times~\frac{1~cm^3}{1000~mm^3} =0.001~cm^3=~0.001~mL\)

  23. aaronq
    • one year ago
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    it is 1000, 10^3= 1000 no?

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