How many moles are in 12.013 x 10 ^24 atoms of helium?

19.948 mol.

Explanation:

Using cross multiplication:

1.0 mole → 6.022 x 10²³ atoms of He.

??? mole → 12.013 x 10²⁴ atoms of He.

∴ The no. of moles of are in  12.013 x 10²⁴ atoms of He = (12.013 x 10²⁴ atoms of He) (1.0 mole) / (6.022 x 10²³ atoms of He) = 19.948 mol.

"you start with 15.67 g mgco3-xh2o, when heated and all the water is removed, you are left with 7.58 g mgco3 only.

therefore, you had 15.67 - 7.58 = 8.09g h2o  

moles of each :

7.58g mgco3 = ? moles = 7.58g / 83.4g/mole = 0.09moles  

8 09g h2o = ? moles = 8.09g / 18g/mole = 0.44moles  

molar ratio between the two by dividing both numbers by the smallest number :

0.09 / 0.09 = 1  

0.44 / 0.09 = 4.8  

mgco3-5h2o"