Question

If mass of 5 mole of $A{{B}_{2}}\text{ }is\text{ 125x1}{{\text{0}}^{-3}}kg$ and mass of 10 mole ${{A}_{2}}{{B}_{2}}\text{ } is \text{ 300x1}{{\text{0}}^{-3}}kg$, then correct molar mass of A and B respectively (in kg/mol):
A. A=$\text{5x1}{{\text{0}}^{-3}}$ and B=$\text{25x1}{{\text{0}}^{-3}}$
B. A=$\text{2}\text{.5x1}{{\text{0}}^{-3}}$ and B=$\text{5x1}{{\text{0}}^{-3}}$
C. A=$\text{2}\text{.5x1}{{\text{0}}^{-3}}$ and B=$\text{10x1}{{\text{0}}^{-3}}$
D. A=$\text{5x1}{{\text{0}}^{-3}}$ and B= $\text{10x1}{{\text{0}}^{-3}}$

Answer 1

Hint: The mass is directly proportional to the mole of a substance and can be easily found out if we know the mole of that compound. The standard unit is 1 mole and so we need to find the answers by evaluating all the formula with respect to 1 mole of a substance.

Complete step by step solution:
-Mole is the amount of substance that contains the atoms, molecules or other particles in an entity equal to the atoms present in 12 g of C-12 isotope. It defines the basis of physical chemistry and so its number is called Avogadro's number which is equal to 6.023x${{10}^{23}}$entities. It is denoted by the symbol ${{N}_{A}}$ .
-Some standard terms used in mole concept are
1 gram-atom = 1 mole atom
1 gram-molecule = 1 mole molecule
1 gram-ion = 1 mole ion
- Avogadro’s number is the number of molecules present in 1 mole which is equal to 6.023x${{10}^{23}}$entities. It is denoted by the symbol ${{N}_{A}}$ . This value is directly used to find the number of atoms in certain different types of molecules which have different representational units.
-The number of moles is given by the formula
\[\text{moles =}\dfrac{wt.\text{ }in\text{ }grams}{\text{molecular wt}\text{.}}\]
-In the question we see that the compounds differ only by the mass of A. So the difference in 1 mole of both the given compounds gives us the value of the mass of A. Once we get the mass of A, we can easily find the value of mass of B by any compound.
-We see that mass of 5 mole of $A{{B}_{2}}\text{ } is \text{ 125x1}{{\text{0}}^{-3}}kg$. So the mass of 1 mole of the same compound will be $\text{25x1}{{\text{0}}^{-3}}$. Similarly, the mass of 10 mole ${{A}_{2}}{{B}_{2}}\text{ } is \text{ 300x1}{{\text{0}}^{-3}}kg$. So the mass of 1 mole of the same compound will be $\text{30x1}{{\text{0}}^{-3}}$ .
-The compounds differ by the mass of A only and so their difference will give us the mass of A. So the mass of A will be $\text{30x1}{{\text{0}}^{-3}}$-$\text{25x1}{{\text{0}}^{-3}}$=$\text{5x1}{{\text{0}}^{-3}}$.
-Now we see that for the compound $A{{B}_{2}}$ , the mass of 1 mole of A and the mass of 2 moles of B give us the total mass of the compound. So the mass of B will be half of the difference in the masses of the whole compound and the mass of A.
-We can write the equation for B as
2xmass of B=Mass of $A{{B}_{2}}$- mass of A
So,2x mass of B=$\text{25x1}{{\text{0}}^{-3}}$-$\text{5x1}{{\text{0}}^{-3}}$=$\text{20x1}{{\text{0}}^{-3}}$
Thus, mass of B = $\text{10x1}{{\text{0}}^{-3}}$

Therefore the correct option is D.

Note: Always make sure that the units are the same in the quantities. Also the same proportion of the quantities are compared for finding any quantity related to both the compounds. Here, we cannot compare the masses of any amount of mole of the compounds. Only 1 mole of the compounds needs to be compared.