Find the total number of atoms in a sample of cocaine hydrochloride, C17H22ClNO4, of mass 21.0 mg .

Answer 1

The number of moles of the compound is 21/molar mass.

There are 45 atoms each molecule of the compound so total number of atoms

= (number of moles) times (Avogadro's number) times 45

Answer 2

One molecule of cocaine hydrochloride contains 17 C atoms + 22 H atoms + 1 Cl atom + 1 N atom + 4 O atoms.

So, one molecule contains 45 atoms.

We are given 21.0 mg of cocaine hydrochloride, so we will find out how many molecules this is, and then find the total number of atoms.

molar mass = 17x12 + 22x1 + 1x35.4 + 1x14 + 4x16 = 204 + 22 + 35.4 + 14 + 64 = 339 (3 sig. figs.)

Converting 21.0 mg to molecules using the molar mass and Avogadro's number, we have...

21.0 mg x 1 g / 1000 mg x 1 mol / 339 g x 6.02x10²³ molecules / mol = 3.73x10¹⁹ molecules

Finally, we convert molecules to atoms:

3.73x10¹⁹ molecules x 45 atoms / molecule = 1.68x10²¹ atoms

Answer 3

Given compound C₁₇H₂₂ClNO₄

We know, moles = mass/ molar mass

molar mass of the given compound= (17x 12) + (22 x1) + (35.5 x1) + (14.0 x1) +( 4 x 16.0) = 339.5 g/mol

so, moles= 21.0 x 10^-3/339.5 =61.9 x 10^-6 moles

In cocaine hydrochloride there are 17 carbon, 22 hydrogen, 1 chlorine, 1 nitrogen, 4 oxygen. adding them up we get total number of atoms, ie, 45 atoms in the molecular formula

To find the total number of atoms, multiply the number of moles, Avogadro number and the number of atoms in the formula

here, total number of atoms in 21.0 g of cocaine hydrochloride is = 61.9 x 10^-6 x 6.022 x10²³ x 45 = 1.68 x 10²¹ atoms