Answer:
3.6 x 10²¹ carbon atoms
Step-by-step explanation:
Data Given:
C₁₂H₂₂O₁₁ = 3.00 x 10²⁰ molecules
Carbon atoms = ?
Solution:
Step 1.
First find number of moles of C₁₂H₂₂O₁₁
Formula used
no. of moles = no. of molecules/ Avogadro's number
Put vales in above formula
no. of moles = 3.00 x 10²⁰ / 6.23 x 10²³
no. of moles = 4.82 x 10⁻⁴ mol
Step 2.
Now find mass of 4.82 x 10⁻⁴ moles of C₁₂H₂₂O₁₁
Molar mass C₁₂H₂₂O₁₁ = 12(12) + 22(1) + 11(16)
Molar mass C₁₂H₂₂O₁₁ = 342 g/mol
Formula used
no. of moles = mass in grams / Molar mass
Put values in formula
4.82 x 10⁻⁴ mol = mass in grams / 342 g/mol
Rearrange the above equation
mass in grams = 4.82 x 10⁻⁴ mol x 342 g/mol
mass in grams = 0.165 g
So,
C₁₂H₂₂O₁₁ = 0.165 g
Step 3.
calculate the percent composition of Carbon (C) in C₁₂H₂₂O₁₁
Since the percentage of compound is 100
So,
Formula used:
Percent Composition of Carbon (C) = mass of carbon / molar mass x 100
Put values in formula
Percent Composition of Carbon (C) = 144 / 342 x 100
Percent of Carbon (C) = 42 %
It means that for ever gram of C₁₂H₂₂O₁₁ there is 0.42 g of C is present.
So,
For the 0.165 g of C₁₂H₂₂O₁₁ the mass of C will be
mass of Carbon (C) = 0.42 x 0.165 g
mass of Carbon (C) = 0.0693 g
Step 5.
Now find the number of moles for 0.0693 g of Carbon (C)
Molar mass of C = 12 g/mol
Formula Used
no. of moles = mass in grams / Molar mass
put values in above formula
no. of moles = 0.0693 g / 12 g/mol
no. of mol = 0.0058
no of moles of Carbon = 0.0058
Step 5.
Now find number of atoms in 0.0058 moles of carbon
Formula used
no. of moles = no. of atoms of C / Avogadro's number
Put vales in above formula
0.0058 = no. of atoms of C / 6.23 x 10²³
Rearrange the above equation
no. of atoms of C = 0.0058 x 6.23 x 10²³
no. of atoms of C = 3.6 x 10²¹
So,
3.6 x 10²¹ carbon atoms are present in 3.00 x 10²⁰ molecules of C₁₂H₂₂O₁₁