Question

Volume of any gas at $95^\circ C$ has $2.9g$ rate which is equal to is $0.184g$ weight of dihydrogen at $17^\circ C$ . Find the molar mass of gas.

Answer 1

We have to know that, The molar mass is the mass of a given synthetic component or synthetic compound ( $g$ ) separated by the measure of substance ( $mol$ ). The molar mass of a compound can be determined by adding the standard nuclear masses (in $g/mol$ ) of the constituent molecules.

Complete answer:
We have to know that, the ideal gas law. This law, the result of the pressing factor and the volume of one-gram atoms of an ideal gas is equivalent to the result of the outright temperature of the gas and the all-inclusive gas consistent.
The formula of ideal gas law has to be given below,
$PV = nRT$
For gas,
Then, the number of moles of the gas ( $n$ ) is,
$n = \dfrac{{Mass}}{{Molar Mass}} = \dfrac{{2.9}}{M}$
Then, the volume of gas ( $V$ ) is,
$V = \dfrac{{nRT}}{p}$
Where,
$T = 95^\circ C = 368K$
Applying $T$ and $n$ values in the above expression,
$V = \dfrac{{2.9R \times 368}}{{MP}}$
For dihydrogen,
The number of moles of hydrogen is,
${n^{'}} = \dfrac{{0.184}}{2} = 0.092$
Then, the volume of dihydrogen ( $V$ ) is,
$V = \dfrac{{nRT}}{p}$
Where,
$T = 17^\circ C = 290K$
Applying $T$ and $n$ values in the above expression. Then, the volume of dihydrogen is,
$V = \dfrac{{0.092R \times 290}}{P}$
Here, at the same pressure, the volume of dihydrogen is equal to the volume of gas.
$0.092R \times 290 = \dfrac{{2.9R \times 368}}{M}$
Therefore, molar mass ( $M$ ) has to be calculated below,
$M = \dfrac{{2.9 \times 368}}{{0.092 \times 290}}$
Hence,
$M = 40$
Thus, the molar mass of the gas is $40g/mol$ .

Note:
We have to know that the ideal gas law is a significant instrument in understanding state connections in vaporous frameworks. For instance, in an arrangement of consistent temperature and pressing factor, the expansion of more gas particles brings about expanded volume.