Question

Find the number of moles of phosphorus in 92.9 g of phosphorus assuming that the molecular formula of phosphorus is ${{P}_{4}}$. Also, determine the number of atoms and molecules of phosphorus in the sample.
A. 3 mol,$7\times {{10}^{23}}$ molecules of ${{P}_{4}}$,$18\times {{10}^{23}}$ atoms of P.
B. 0.75 mol,$4.52\times {{10}^{23}}$ molecules of ${{P}_{4}}$,$12\times {{10}^{23}}$ atoms of P
C. 0.75 mol,$4.52\times {{10}^{23}}$ molecules of ${{P}_{4}}$,$18.04\times {{10}^{23}}$ atoms of P
D. None of these

Answer 1

Hint: Calculate the number of moles from the information, then find out the number of molecules, and multiply it with the atomicity to get the number of atoms in the molecule.

Complete step-by-step answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question. We know that the atomic mass of a P atom is 31 grams. So for the ${{P}_{4}}$ molecule, the mass is ($31\times 4$) which is 124 grams. As the given mass is 93 grams, so the number of moles is $\dfrac{93}{124}=0.75$.
Now, 1 mole of ${{P}_{4}}$ contains $6\times {{10}^{23}}$ molecules
So, 0.75 mole of ${{P}_{4}}$ should contain ($0.75\times 6\times {{10}^{23}}$) atoms, which is $4.5\times {{10}^{23}}$molecules
Finally, we calculate the number of atoms from the molecules, which is ($4.5\times 4\times {{10}^{23}}$) which is $18.04\times {{10}^{23}}$ atoms.

So, we get our correct answer for the question to be option C.

Note: It is to be noted that in case of a molecule, to find out the molar mass, the masses of individual elements are added up. For example, ${{H}_{2}}O$ molar mass is $(2\times 1)+16$ which comes out as 18 grams.