Question

A sample of phosphorus has 0.5 moles of P4 , molecules
(0) How many P4 molecules are there?
(ii) How many P atoms are there?
(iii) How many moles of P atoms are there in the sample?
(iv) What is the mass of the sample?

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Answer 1

Answer:

Explanation:

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Answer 2

(i) $3.011\times 10^{23} \;molecules\; of\; P_4$

(ii) $12.044\times10^{23}\;of\;P\;atoms$

(iii) $2\;moles\;of\;P\;atoms$

(iv) 24 g

• The mole concept is a concept in chemistry which was introduced to provide a method of expressing substances or elements as an amount of atoms present in it.
• There are several elements in chemistry that are listed out in what is called as the periodic table and at the molecular level, even if a small fraction of the element or a sample is taken it can be observed that, that portion of the element also consists of several number of atoms.
• Therefore, in order to measure this amount of atoms or entities present in a gram of an element was known by a unit of measurement termed as 'mole'.
• A mole is defined to be the equivalent of the amount of substance that consists of the same amount of units or entities contained in exactly 12 g of a Carbon atom.
• The amount of atoms contained in 12 g of a Carbon atom is given exactly by a constant known as the Avogadro number or the Avogadro constant whose standard value is fixed given to be $6.02214076 \times 10^{23}$. The Avogadro number is denoted as $N_A$.
• So the mole of every element is compared with the mass and the number of atoms present in a carbon-12 sample.
• The number of moles will hence be given as the total number of atoms present in the Carbon-12 sample.
• This means that the number of moles will be equal to the the mass of 12 g of Carbon atom that contains Avogadro number of atoms present in it.

Thus, the formula is given as:

$Number\; of\; entities = Number\; of\; moles \times Avogadro\; constant$

$N=n\times N_A$  -------------(1)

Here, the term entities refers to atoms, molecules, monoatomic or polyatomic substances etc.

It is given that the sample of Phosphorous consists of 0.5 moles of $P_4$ molecules.

(i) The number of $P_4$ molecules present is to be found out. Thus by applying the formula in equation (1) we have:

$N=n\times N_A$

Here, N which is the number of $P_4$ molecules is to be calculated.

Given, $n=0.5\; moles$ and $N_A=6.022\times 10^{23}$

By substituting we get:

$N=0.5\times6.022\times 10^{23}$

$\implies N\;of\;P_4=3.011\times 10^{23} \;molecules$

(ii) The number of $P_4$ atoms is to be found out. It is known that the $P_4$ molecule consists of 4 atoms in total.

We know that 0.5 moles, that is 1 molecule of $P_4$ had $3.011\times 10^{23} \;molecules$. Thus we have:

Number of atoms in 1 $P_4$ molecule = 4 atoms

⇒Number of atoms present in $3.011\times 10^{23} \;molecules$ of $P_4$ = x atoms

$\implies x=3.011\times 10^{23} \times 4\;atoms=12.044\times10^{23}\;atoms$

Thus, the umber of P atoms in 0.5 moles of Phosphorus has $12.044\times10^{23}\;atoms$.

(iii) We know that from the mole concept:

$6.022\times 10^{23}\;atoms=1\;mole$

So, in $12.044\times10^{23}\;atoms$ the number of moles contained is given as:

$n=\frac{12.044\times10^{23}}{6.022\times 10^{23}}=2\; moles$

So, number of moles in P atoms are 2 moles.

(iv) The atomic mass of P is said to be 31 and hence the molecular of $P_4$ will be $31\times 4=124$ as there are 4 atoms that make up the $P_4$ molecule.

So, we know that 1 mole of $P_4$ = 124 g

⇒0.5 moles of $P_4$ = ?

Thus, we have: $=0.5\times 124=62g$

So the mass of the sample of phosphorous will be 24 g.

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