Question

The density of a gas is 16 at NTP. At what temperature its density will be 14 if the pressure remains constant?
A.${50^o}C$
B.${39^o}C$
C.${57^o}C$
D.${43^o}C$

Answer 1

Hint: To answer this question, you should recall the concept of the ideal gas equations. Use the gas laws to find the answer to this question:

Formula used: \[\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{T_2^{}}}\]
${T_1}$=Initial temperature, ${V_1}$=Initial volume, ${T_2}$=Final temperature and ${V_2}$=Final Volume

Complete step by step solution:
We know that the Ideal Gas Equation is:
\[PV = nRT\]
where $P$ is pressure, $V$ is volume, $R$ is the universal gas constant, $n$ is no. of moles and $T$ is temperature
Since pressure is constant, we can use Charles' law to obtain the temperature:
 \[\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{T_2^{}}}\].
Since molecular mass is constant:
\[{\rho _1}{T_1} = {\rho _2}{T_2}\] ${\text{since }}\left( {{\text{V = }}\dfrac{{{\text{mass}}}}{{{\text{density}}}}} \right)$
Substituting the appropriate values:
\[ \Rightarrow 16 \times 273 = 14 \times {T_2}\]
After solving we get,
\[ \Rightarrow {T_2} = 312\;K = {39^o}\;C\].

Hence, the correct answer to this question is B.

Note: Make sure you remember that at conditions of high temperature and lower pressure, a real gas behaves like an ideal gas, because the potential energy due to intermolecular attractive forces becomes less significant compared with the particles’ kinetic energy, and the size of the molecules becomes less significant compared to the space between them. Along with different speeds, you should know the concept of the Maxwell-Boltzmann equation. The five gas laws are:
1.Boyle’s Law establishes a relationship between the pressure and the volume of a gas.
2.Charles’s Law establishes a relationship between the volume occupied by a gas and the absolute temperature.
3.Gay-Lussac’s Law establishes a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
4.Avogadro’s Law establishes a relationship between the volume occupied by a gas and the amount of gaseous substance.
5.After combining these four aforementioned laws we arrive at the Combined Gas Law