Question

To what temperature must a neon gas sample be heated to double its pressure if the initial volume of gas at ${75^0}C$ is decreased by 15.0% by cooling the gas?
A. 592 K
B. 492 K
C. 542 K
D. 642 K

Answer 1

Hint- In order to deal with this question first we will relate the relation between two volumes according to the given problem statement, then we will apply the gas equation to calculate the required temperature.

Complete answer:
Formula used- $\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
Given that Initial temperature is ${T_1} = {75^0}C$
Let us assume Initial volume is ${V_1}$ and Initial pressure is ${P_1}$ .
Given that the final pressure is double the initial pressure.
${P_2} = 2{P_1}$
According to the question statement
Initial temperature in Kelvin is: ${T_1} = 75 + 273 = 348K$
And the relation between volumes will be:
Final volume = initial volume – 15% of initial volume.
$
   \Rightarrow {V_2} = {V_1} - \dfrac{{15}}{{100}}{V_1} \\
   \Rightarrow {V_2} = \dfrac{{100{V_1} - 15{V_1}}}{{100}} \\
   \Rightarrow {V_2} = \dfrac{{85{V_1}}}{{100}} \\
 $
According to the gas law the relation between temperature and volume is
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
Now in order to find the required final temperature we will apply gas equation and substitute all the values given:
\[
  \because \dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}} \\
   \Rightarrow \dfrac{{{P_1}{V_1}}}{{348}} = \dfrac{{2{P_1} \times \left( {\dfrac{{85{V_1}}}{{100}}} \right)}}{{{T_2}}} \\
   \Rightarrow \dfrac{{{P_1}{V_1}}}{{348}} = \dfrac{{2{P_1} \times 85{V_1}}}{{100 \times {T_2}}} \\
   \Rightarrow {T_2} = \dfrac{{2 \times 85 \times 348}}{{100}} \\
   \Rightarrow {T_2} = 591.6K \\
   \Rightarrow {T_2} \approx 592K \\
 \]
Hence, neon gas sample should be heated to 592 K

So, the correct answer is option A.

Additional information-
Neon is a chemical compound with the atomic number 10 and the symbol Ne. It is an aristocratic flame. Neon is a colourless, odorless, neutral monatomic gas in normal conditions, with air density of around two-thirds. It was discovered in 1898 (along with krypton and xenon) as one of the three remaining latent rare inert elements in dry air, following depletion of nitrogen , oxygen, argon and carbon dioxide. Neon was the second of these three rare gases to be discovered, and was recognised as a new element by the vivid red spectrum of emissions.

Note- If temperature and pressure are kept constant otherwise the gas volume is directly proportional to the number of gas molecules. If the temperature and volume remain stable otherwise the gas changes pressure is directly proportional to the number of gas molecules present. The ideal gas law, also known as the general gas equation, is the equation of state of an ideal hypothetical gas. It is a good approximation of many gases' behavior under many conditions, though it has several limitations.