Question

A sample of sucrose is found to contain 72.28 into 10 to the power 21 atoms of carbon find the mass of sample in grams

Answer 1

Hello Dear.

Here is the answer---

No. of atoms of Carbon in certain amount of Sucrose = 72.28 × 10²¹ atoms.
Molar Mass of the Carbon = 12 g/mole.
Avogadro's No.(Nₐ) = 6 × 10²³

Now, Using the Formula,

No. of atoms = (Mass/Molar Mass) × Nₐ
72.28 × 10²¹ = (Mass/12) ×  6 × 10²³
⇒72.28 × 2 = Mass × 100
⇒ Mass = 1.44 g.

Now,
Molar Mass of the Sucrose (C₁₂H₂₂O₁₁) = 342 g/mole.
Mass of Carbon Present in 1 mole of Sucrose = 12 × 12
 = 144 g.

Now,
144 g of Carbon is present in 1 mole(342 g) of Sucrose.
∴ 1 g of the Carbon is present in 342/144 g of Sucrose.
∴ 1.44 g of Carbon is present in (342/144) × 1.44 g of Sucrose.
      = 3.42 g of Sucrose. 

∴ Mass of the Sample of Sucrose is 3.42 grams.


Hope it helps.

Answer 2

Molecular formula of sucrose = C₁₂H₂₂O₁₁
∵ 1 Molecule of sucrose has 12 atoms of carbon .
∴ 1 mole of sucrose contains 12 mole of Crabon atoms .

First of all we have to find out number of mole of C - atoms
given, number of C - atoms in sucrose sample = 72.28 × 10²¹
so, number of mole of C- atoms in sample = 72.28 × 10²¹/6.023 × 10²³
= 12 × 10⁻² = 0.12 mole

∴ number of mole of sucrose sample = number of mole of C-atoms /12
= 0.12/12 = 0.01 mole
Now, mass of sucrose sample = numbe of mole × molecule mass of sucrose.
= 0.01 × 342 [ ∵ molecular mass of sucrose = 342g/mol ]
= 3.42 g

Hence, mass of sucrose sample is 3.42g