Question

Calculate the volume in litres of $49.8{\text{ }}gram$ of $HCl$ gas at STP (molar mass of $HCl$ =$1{\text{ }} atmosphere,i.e.,760{\text{ }}mm{\text{ }}Hg$.

Answer 1

At standard Temperature and Pressure (STP) the volume occupied by one mole of any gas is $22.4{\text{ }}litres$ This volume is called the standard molar volume. It is said that $22.4{\text{ }}litres$ of any gas at STP weighs equal to its molecular mass in grams.

Complete Step by step answer: At standard temperature (STP) is an elementary concept. In the STP system, both pressure and temperature are in their typical form. Temperature of this system is considered as $273{\text{ }}Kelvin{\text{ }}or{\text{ }}{0^o}C$ and Standard pressure is $1{\text{ }} atmosphere,i.e.,760{\text{ }}mm{\text{ }}Hg$. Then experimentally, one mole of any gas occupies a volume of $22.4{\text{ }}litres$ at $273{\text{ }}Kelvin$ and $1{\text{ }}atmosphere$. The equation can be expressed
($1{\text{ }}mole{\text{ }}of{\text{ }}gas{\text{ }}at{\text{ }}STP = 22.4{\text{ }}litres{\text{ }}of{\text{ }}gas.)$
Now we can calculate the volume of $22.4{\text{ }}litres$ of the gas at S.T.P from the given weight.

Given, According to the question, the weight of $HCl$ gas at STP = $49.8{\text{ }}gram$
Molar mass of $HCl$= ($36.5g - mo{l^{ - 1}})$
Now $22.4{\text{ }}litres$ of any gas at S.T.P. weighs equal to its molecular mass in grams.
$\;\;\therefore 36.5g\;occupies\; = 22.4{\text{ }}litres{\text{ }}of{\text{ }}volume$
∴ $49.8{\text{ }}gram$ of $HCl$occupies =$\dfrac{{49.8 \times 22.4}}{{36.5}}$ $= 30.56litres.$
So the volume in litres of $49.8{\text{ }}gram$ of $HCl$ gas at STP = $= 30.56litres.$

Note: STP conditions are often used for engineering calculations for a gas flow or gas volume is involved. When gas volume is considered at a fixed reference temperature & pressure, its 'standard volume' is directly proportional to the molar quantity. Gas density measured at STP conditions is also a good measure of the composition of that gas, another common form of STP called standard ambient temperature and pressure or S.A.T.P. is used.