Question

If one cubic dm of a gas weighs \[{{2}}{{.5}}\,{{g}}\] at STP, its molecular weight (in grams) is:
A. \[{{56}}\,{{g}}\]
B. \[11.2\,{{g}}\]
C. \[22.4\,{{g}}\]
D. \[224\,{{g}}\]

Answer 1

Hint:Molecular weight measures the mass or weight of a given species or a molecule. It is represented in the unit of \[{{Da}}\,\] or \[{{\mu }}\].

Complete step by step answer:
Given that,
\[{{1}}\,{{d}}{{{m}}^{{3}}}\] weighs \[{{2}}{{.5}}\,{{g}}\],
 then we can say that \[{{22}}{{.4}}\,{{d}}{{{m}}^{{3}}}\] weighs,
\[{{22}}{{.4}}\, \times 2.5 = \,56\,{{g}}\]
Now,
We know that 1 mole of gas at STP occupies \[{{22}}{{.4}}\,{{d}}{{{m}}^{{3}}}\]
As we know that, the molecular weight is defined as the weight of 1 mole of the gas, so we can say that the required weight is \[{{56}}\,{{g}}\] if one cubic dm of a gas weighs \[{{2}}{{.5}}\,{{g}}\] at STP.
Therefore, we can conclude that out of the given four options, A is the correct option. B, C and D are incorrect options.

Additional information:
Full form of STP is standard temperature and pressure. STP is a condition that helps in comparing measurements between various sets of given data. Earlier until 1982, the STP was measured as the temperature of \[{{273}}{{.15}}\,{{k}}\left( {{{0^\circ C,}}\,{{32^\circ F}}} \right)\] and an pressure of\[{{1}}\,{{atm}}\left( {{{101}}{{.325}}\,\,{{kPa}}} \right)\] exactly.. But IUPAC has defined that STP is a temperature of \[{{273}}{{.15}}\,{{k}}\left( {{{0^\circ C,}}\,{{32^\circ F}}} \right)\] and an pressure of \[{{1}}{{{0}}^{{5}}}{{Pa}}\left( {{{100}}\,{{kPa,}}\,{{1}}\,{{bar}}} \right)\] exactly since 1982.

Note: Molecular weight is also known as molecular mass. It is the mass of a substance which is based on the atomic weight of 12- carbon which is 12. Molecular weight is the total weight after summing up the atomic weights of all the atoms present in the molecular formula of a compound. For example we can calculate the molecular mass of glucose in the following way.