Question

If the weight of 5.6 litres of a gas at S.T.P. is 11 grams, the gas is:
A.Phosphine
B.Phosgene
C.Nitric oxide
D.Nitrous oxide

Answer 1

Hint: The volume occupied by one mole of any gas under S.T.P. is $22.4$ litres. This volume is called the standard molar volume. It is said that $22.4$ litres of any gas at S.T.P. weighs equal to its molecular mass in grams.

Complete step by step answer:
The term S.T.P. means ‘standard temperature and pressure’.
The standard temperature is 273 K and the standard pressure is arbitrarily defined as 1 atmosphere or 760 mm.
Thus, one mole of any gas occupies a volume of $22.4$ litres at 273 K and 1 atmosphere.
Calculate the weight of $22.4$ litres of the gas at S.T.P. from the given weight:
Now, according to the given question, the weight of $5.6$ litres of a gas at S.T.P. is 11 grams. This means that $5.6$ litres of a gas at S.T.P. weigh 11 grams.
So, the weight of 1 litre of the gas at S.T.P. is equal to $\dfrac{{11}}{{5.6}}$ g.
Therefore, the weight of $22.4$ litres of the gas at S.T.P. is equal to
 $
   = \dfrac{{11 \times 22.4}}{{5.6}}{\text{g}} \\
   = 44{\text{g}} \\
 $
This weight must be equal to the molecular mass of the gas.
Now, the molecular mass of phosphine $\left( {{\text{P}}{{\text{H}}_{\text{3}}}} \right)$ is $ = 31 + 3 \times 1 = 34$ g per mol.
The molecular mass of phosgene $\left( {{\text{COC}}{{\text{l}}_{\text{2}}}} \right)$ is $ = 12 + 16 + 2 \times 35.5 = 99$ g per mol.
The molecular mass of nitric oxide $\left( {{\text{NO}}} \right)$ is $ = 14 + 16 = 30$ g per mol.
The molecular mass of nitrous oxide $\left( {{{\text{N}}_2}{\text{O}}} \right)$ is $ = 14 \times 2 + 16 = 44$ g per mol.
Thus, the molecular mass of nitrous oxide matches the weight of $22.4$ litres at S.T.P. So, the gas is nitrous oxide.

Therefore, the correct option is D.

Note: Standard conditions of temperature and pressure are often used in industry and commerce to define the standard reference conditions to express the volumes of liquids and gases and related quantities like the rate of volumetric flow as they are highly dependent on temperature and pressure. Since laboratory conditions rarely involve S.T.P., another common form of S.T.P. called the standard ambient temperature and pressure or S.A.T.P. is used. It has a temperature of $298.15$ K and pressure of exactly 1 atm.