a) Molecular formula
Procedure
You need to pass the information in grams to moles.
Then you need to find the proportion of moles, which will give you the subscript for each element in the formula, and then you will have the empirical formula.
With this you need to calculate the molar mass of the empirical formula.
Then divide the molar mass of the compound by the molar mass of the empirical formula to find the multiple that you have to use to establish the molercular formula.
Solution
Number of moles of an element = mass in grams / atomic mass
C: 38.67 g / 12 g/mol = 3.2225 moles
H: 16.22 g / 1 g/mol = 16.22 moles
N: 45.11 g / 14 g/mol = 3.2221 moles
Proportions: divide by the smaller number of moles
C: 3.2225 / 3.2221 = 1.0
H: 16.22 / 3.2221 = 5.0
N: 3.2221 / 3.2221 = 1.0
Empirical formula: C1H5N1
Empirical mass: 1mol*12g/mol + 5mol*1g/mol + 1 mol*14g/mol = 31 g/mol
Number of times the empirical formula is contained in the molecular formula: formula mass / empirical mass = 62.12 g/mole/31g/mole = 2
Molecular formula = 2* empirical formula = C2H10N2.
2) H atoms
Proportion of H: 10 moles of H / 62.12 g of C2H10N2 = x g of H / 35.0 g of C2H10N2
Solve for x:
x = 35.0*10 / 62.12 = 5.63 moles
Number of atoms = number of moles * Avogadro = 5.63 * 6.02 * 10^23 atoms
= 33. 89 * 10^23 atoms = 3.389 * 10^24 atoms
