Question

One litre of a gas is collected at STP. What would be the volume of the same gas at 2 atmospheric pressure and $\text{27 }\!\!{}^\circ\!\!\text{ C}$:
(A) $\dfrac{\text{300}}{\text{2 }\!\!\times\!\!\text{ 273}}\text{ litre}$
(B) $\dfrac{\text{2 }\!\!\times\!\!\text{ 300}}{\text{273}}\text{ litre}$
(C) $\dfrac{\text{273}}{\text{2 }\!\!\times\!\!\text{ 300}}\text{ litre}$
(D) $\dfrac{\text{2 }\!\!\times\!\!\text{ 273}}{\text{300}}\text{ litre}$

Answer 1

Hint: Recollect the concept of STP. Find out the difference between STP and NTP. The question says 1 litre of gas is collected at STP and we need to find the volume of the same gas at different conditions of temperature and pressure. By using combined gas law, we can relate pressure, volume and temperature at two different conditions. Use this law and just substitute the values to get the answer.

Complete step by step solution:
STP stands for standard temperature pressure which is a standard set of reaction conditions of experimental data for establishing a comparison between a wide range of data sets. At STP, the temperature is 273K and pressure is 1atm.
NTP stands for normal temperature pressure wherein temperature is 293K and pressure is 1atm.
In the given question, we have to write the initial and the final conditions at first. So, the initial conditions go as follows:
The Initial Pressure or ${{\text{P}}_{\text{1}}}$is 1 atm,
The Initial Volume or ${{\text{V}}_{\text{1}}}$is 1 Litre,
The Initial Temperature or ${{\text{T}}_{\text{1}}}$ is 273 K.
Now the final conditions are given as:
The Final Pressure or ${{\text{P}}_{\text{2}}}$ is 2 atm,
The Final Volume of ${{\text{V}}_{\text{2}}}$ is to be found out by us.
The Final Temperature or ${{\text{T}}_{\text{2}}}$ is (273 + 27) = 2 = 300 K
By Combined Gas Law we have,
$\dfrac{{{\text{P}}_{\text{1}}}{{\text{V}}_{\text{1}}}}{{{\text{T}}_{\text{1}}}}\text{ = }\dfrac{{{\text{P}}_{\text{2}}}{{\text{V}}_{\text{2}}}}{{{\text{T}}_{\text{2}}}}$
Now substituting the values in the above equation, we get:
$\begin{align}
& \dfrac{\text{1 }\!\!\times\!\!\text{ 1 }}{\text{273}}\text{ = }\dfrac{\text{2 }\!\!\times\!\!\text{ }{{\text{V}}_{\text{2}}}}{\text{300}} \\
& {{\text{V}}_{\text{2}}}\text{ = }\dfrac{\text{300}}{\text{2 }\!\!\times\!\!\text{ 273}}\text{ litre} \\
\end{align}$

Hence, we can say that the correct answer is Option A.

Note: STP is standards set by the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST). By using combined gas law which gives the relationship between pressure, volume and temperature, these kinds of problems can be easily solved.