Respuesta :
Answer is: the total number of atoms in a sample of cocaine hydrochloride is 1.65·10²¹.
m(C₁₇H₂₂ClNO₄) = 21.0 mg ÷ 1000 mg/g.
m(C₁₇H₂₂ClNO₄) = 0.021 g; mass of cacaine hydrochloride.
n(C₁₇H₂₂ClNO₄) = m(C₁₇H₂₂ClNO₄) ÷ M(C₁₇H₂₂ClNO₄).
n(C₁₇H₂₂ClNO₄) = 0.021 g ÷ 339.8 g/mol.
n(C₁₇H₂₂ClNO₄) = 0.000061 mol = 6.1·10⁻⁵ mol.
N(C₁₇H₂₂ClNO₄) = n(C₁₇H₂₂ClNO₄) · Na (Avogadro constant).
N(C₁₇H₂₂ClNO₄) = 6.1·10⁻⁵ mol · 6.022·10²³ 1/mol.
N(C₁₇H₂₂ClNO₄) = 3.67·10¹⁹; number of molecules.
In one molecule of cocaine hydrochloride there are 45 atoms (17 carbons, 22 hydrogens, 1 chlorine, 1 nitrogen and 4 oxygens):
N(atoms) = N(C₁₇H₂₂ClNO₄) · 45.
N(atoms) = 3.67·10¹⁹ · 45.
N(atoms) = 1.65·10²¹.
Answer: The number of atoms in given amount of cocaine hydrochloride is [tex]1.674\times 10^{21}[/tex]
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Given mass of cocaine hydrochloride = 21.0 mg = 0.021 g (Conversion factor: 1 g = 1000 mg)
Molar mass of cocaine hydrochloride = 339.8 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of cocaine hydrochloride}=\frac{0.021g}{339.8g/mol}=6.18\times 10^{-5}mol[/tex]
In 1 mole of cocaine hydrochloride, 17 moles of carbon atom, 22 moles of hydrogen atom, 1 mole of chlorine atom, 1 mole of nitrogen atom and 4 moles of oxygen atoms are present
Total number of atoms in 1 mole of cocaine hydrochloride = (17 + 22 + 1 + 1 + 4) = 45 atoms
According to mole concept:
1 mole of a substance contains [tex]6.022\time 10^{23}[/tex] number of atoms.
So, [tex]6.18\times 10^{-5}mol[/tex] of cocaine hydrochloride will contain = [tex](6.18\times 10^{-5}\times 45\times 6.022\times 10^{23})=1.674\times 10^{21}[/tex] number of atoms
Hence, the number of atoms in given amount of cocaine hydrochloride is [tex]1.674\times 10^{21}[/tex]
