Question

Complete the following calculations.
Calculate the mass of calcium that will contain the same number of atoms as are present in 3.2 gm of Sulphur. [Atomic mass : S=32, Ca=$40g\text{ }mol{{e}^{-1}}$]

Answer 1

Hint: If we have the same number of atoms of the two elements i.e. Sulphur and calcium, then their number of moles should also be equal to each other and we can find the moles by using the formula as: $\dfrac{Given\text{ }mass}{molar\text{ }mass}$ and then by comparing , we can easily find the mass of calcium atom. Now answer it.

Complete step by step answer:
We can solve this in the following way as;
The atomic mass of Sulphur=32g (given)
As in the question; it is said that the number of the atoms of the Sulphur is equal to the number of atoms of the calcium’
So, then; the moles of both Sulphur and calcium must be equal to each other i.e.
The moles of Sulphur = the moles of the calcium ----------(1)
Now, we will first calculate the moles of Sulphur;
Moles of the Sulphur =$\dfrac{Given\text{ }mass}{molar\text{ }mass}$ ----------(2)
As we know,
Mass of Sulphur= 3.2g (given)
Molar mass of Sulphur= 32 g (given)
Then, put these values in equation (1); we get
Moles of the Sulphur =$\dfrac{3.2}{32}=0.1\text{ }mole$ ----------(3)
Similarly, we will calculate the moles of calcium as;
Mass of calcium = x g
Molar mass of calcium = 40 g (given)
Moles of the calcium =$\dfrac{x}{40}mole$ -------------(4)
Now, put the values of equation (3) and (4) in equation (2), we get;
$\begin{align}
& 0.1=\dfrac{x}{40} \\
& x=40\times 0.1 \\
& x=4g \\
\end{align}$

Therefore, the mass of calcium that will contain the same number of atoms as are present in 3.2 gm of Sulphur is 4 gram.

Note: Keep in mind the moles of the two atoms will be equal to each other only in that case when we have been given that both the elements contain equal number of the atoms i.e. Avogadro number of atoms.