Question

Bell metal contains 80 % copper. The mass of Bell metal which contains $15 \times {10^{20}}$ atoms of copper is ( Cu = 64 ).
a.) 2 mg
b.) 20 mg
c.) 40 mg
d.) None of these

Answer 1

Hint: We have studied that 1 mole of a substance has Avogadro’s number of atoms or molecules and is equal to the molar mass of the element. From this, we can find the number of moles of a given atom. And then the mass can be calculated by the product of the number of moles with a molar mass of the element.

Complete step by step answer:
We know that 1 mole of a substance has Avogadro’s number of atoms or molecules and is equal to the molar mass of the element.
As we have copper metal, molar mass of Cu = 64
So, this means 1 mole of Cu has = $6.022 \times {10^{23}}$atoms
We have in the question, $15 \times {10^{20}}$ atoms.
So, this means it will have number of moles as -
$15 \times {10^{20}}$ atoms will have moles = $\dfrac{{15 \times {{10}^{20}} \times 1}}{{6.022 \times {{10}^{23}}}}$
$15 \times {10^{20}}$ atoms will have moles = 0.00249 moles
Further, we know that the number of moles = $\dfrac{{Given{\text{ mass}}}}{{Molar{\text{ mass}}}}$
So, the mass of Cu atoms = Moles $ \times $ Molar mass
mass of Cu atoms = 0.00249$ \times $ 64
mass of Cu atoms = 0.159 g
Thus, $15 \times {10^{20}}$atoms of Cu has mass = 0.159 g
This is 80 % of the piece of metal,
weight of the mass is 100 % = $\dfrac{{100}}{{80}} \times 0.159$ = 0.198 g
So, the piece of metal has mass = 0.198 g = 198 mg

Thus, the correct answer is the option d.).

Note: It must be noted that One mole of any element has Avogadro’s number of atoms, and in case we have a molecule then, 1 mole of a molecule is equal to Avogadro’s number of molecules. Further, 1 gram has 1000 milligrams. So, the weight in milligrams can be found by multiplying with 1000.