## 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.

1. aaronq

first find the volume of the cube, then find the mass with the density, finally convert the mass to moles

2. anonymous

How do you find the volume?

3. aaronq

|dw:1442365426768:dw|

4. anonymous

So do you find the mass by using the density formula?

5. aaronq

yep

6. aaronq

you'll have to convert the volume (or the density) to match the units

7. anonymous

I'm trying to work it out and getting confused.

8. anonymous

$\sf \rho = \frac{m}{v} \\ \rho = 120~\frac{g}{mL}~,~~v =(1mm)^3$ $\sf 1~mm^3 ~\times~ \left(\frac{1~cm}{1~mm}\right)^3~\times~\frac{1~mL}{1~cm^3} =~1~mL$ $\sf \frac{120~g}{mL} =\frac{m}{1~mL}~\implies m = 120~g$

9. anonymous

When I see a value or conversion factor, I typically try to associate it with an appropriate formula

10. aaronq

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. anonymous

...it was a typo <_<

12. aaronq

suuuuure it was :P

13. aaronq

A+ for effort

14. anonymous

Um...which way is it?

15. anonymous

The way @aaronq wrote.

16. anonymous

Thanks

17. anonymous

Would it be 1000 or 100 for cm^3?

18. anonymous

Alright. I was wondering why there was an extra 0

19. anonymous

Thanks for the help!

20. anonymous

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. anonymous

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

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

it is 1000, 10^3= 1000 no?