# Suppose that A and B form the compounds ${ B }_{ 2 }{ A }_{ 3 }$ and ${ B }_{ 2 }{ A }$ . If 0.05 mol of ${ B }_{ 2 }{ A }_{ 3 }$ weighs 9 g and 0.1 mole of ${ B }_{ 2 }{ A }$ weighs 10 g, the atomic weight of A and B respectively are:

(A) 30 and 40

(B) 40 and 30

(C) 20 and 5

(D) 15 and 20

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**Hint:**For any compound, its molar mass is calculated by adding the masses of particular elements in it (taking consideration of atomicity as well). Here in this question, make two equations out of the two compounds (${ B }_{ 2 }{ A }_{ 3 }$ ,${ B }_{ 2 }{ A }$ ) and then equate it.

**Complete step by step answer:**

Let us consider, ‘x’ as atomic weight of A and ‘y’ as atomic weight of B.

As it is already given in the question that 0.5 mol of ${ B }_{ 2 }{ A }_{ 3 }$ weighs 9 g.

Therefore 1$\left( 0.05\ \times \ 20 \right) $ mol of ${ B }_{ 2 }{ A }_{ 3 }$ will weigh $\left( 9\ \times \ 20 \right) $ g = 180 g.

Put ‘x’ and ‘y’ as masses of A and B respectively and then write the equation as given below:

${ 2x\ +\ 3y\ = }$ mass of 1 mol of ${ B }_{ 2 }{ A }_{ 3 }$ = 180 g

${ \Rightarrow \ 2x\ +\ 3y\ =\ 180 }$ (i).

Similarly it's given that 0.1 mole of ${ B }_{ 2 }{ A }$weighs 10 g.

Therefore 1$\left( 0.1\ \times \ 10 \right) $ mol of ${ B }_{ 2 }{ A }$ will weigh $\left( 10 \ \times \ 10 \right) $g = 100 g.

Put ‘x’ and ‘y’ as masses of A and B respectively and then write the equation as given below:

${ 2y\ +\ x\ = }$ mass of 1 mol of ${ B }_{ 2 }{ A }$= 100g

${ \Rightarrow 2y\ +\ x\ =\ 100 }$ (ii).

Equate both the equations (i) and (ii),

We will get x = 40 and y = 30.

Therefore from the above atomic masses of A and B are 40 and 30 respectively, which has been satisfied by Option (B).

**The answer for this question is Option (B) 40 and 30.**

**Additional Information:**

Mole : one mole is defined as the mass of an avogadro number of particles (atoms or molecules) or it is defined as the amount of particles present as that in 12 g of carbon-12 isotope.

Avogadro’s number: ${ 6.022\ \times \ { 10 }^{ 23 }}$ or${ 6.022\ \times \ { 10 }^{ 23 } }\ { mol }^{ -1 }$ .

Molar mass is defined as the mass of one mole of a substance. For example, the molecular weight of ammonia is 17 atomic mass units (amu) so its molar mass is 17 g.

Formula mass is also similar to molar mass but is used in the case of ionic compounds. Eg: Formula mass of NaCl is 23 + 35.5 = 58.5 u.

Gram atomic mass is the term used when atomic mass is expressed in grams.

Eg : gram atomic mass of Carbon is 12g.

Number of moles present in a compound can be found by the following equations:

${ number\ of\ moles\ =\ \frac { given\ mass }{ molar\ mass } \ =\ \frac { given\ volume\ at\ STP }{ molar\ mass\ at\ STP } \ =\ \frac { given\ mass }{ avogadro\ number } }$

**Note:**Mass of one mole of a compound can be found easily by adding the molar mass of the elements present in it. But we need to be careful when the mass is given other than the one mole .For Eg: If the mass given is that of half mole of a compound, we need to do accordingly as we have solved the question.