Question

At $T\left( K \right)$ , he ratio of kinetic energies of $4g$ of ${{H}_{2\left( g \right)}}$ and $8g$ of ${{O}_{2\left( g \right)}}$ is:
A.$1:4$
B.$4:1$
C.$2:1$
D.$8:1$

Answer 1

Hint: kinetic energy is an energy which is possessed by the motion of an object. Unit of kinetic energy is $kg{{m}^{2}}/{{s}^{2}}$ .
$K.E=\dfrac{3}{2}nRT$
Here, $n$ denotes as no of moles, $R$ denotes as universal gas constant, $T$ denotes as temperature of the system.
Formula used
$n=\dfrac{w}{m}$
Where, $w$is the weight of a compound in $g$
$m$ is the molar mass of an compound

Complete step by step answer:
As we have discussed earlier that $K.E=\dfrac{3}{2}nRT$
Where, kinetic energy is directly proportional to no. of moles of a compound
$\dfrac{K.{{E}_{{{H}_{2}}}}}{K.{{E}_{{{O}_{2}}}}}=\dfrac{{{n}_{{{H}_{2}}}}}{{{n}_{{{0}_{2}}}}}$
$\dfrac{{{n}_{{{H}_{2}}}}}{{{n}_{{{O}_{2}}}}}=\dfrac{\dfrac{4}{2}}{\dfrac{8}{32}}=\dfrac{8}{1}$
Therefore, the correct option is $\left( D \right)$ that is $8:1$ .

Additional information
A mole is defined as the standard scientific unit of measuring small entities like atoms and molecules. It is the most convenient to calculate the amount of products and reactants in a chemical reaction. It is the SI unit of the amount of the substances present in the reaction. One mole contains $6.022\times {{10}^{23}}$ . This number is known as the Avogadro constant. The avogadro's number is for atoms, molecules, electrons and ions.
Molar mass is defined as the total mass of a compound divided by the amount of substance present in the sample. The SI unit of molar mass is $kg/mol$. Here molar mass of ${{H}_{2}}$ is $4$ and molar mass of ${{O}_{2}}$ is $32$ .

Note:
The atomic mass is the mass of an atom whereas the atomic weight is the weighted average of naturally occurring isotopes. For example , here $4g$ is the atomic weight of the ${{H}_{2}}$ and $4$ is the atomic mass of an ${{H}_{2}}$ .
At given temperature the average kinetic energy of a gas molecule is constant.