Question

A \[0.5~d{{m}^{3}}~\] flask contains gas \[A\] and \[1~d{{m}^{3}}~\] flask contains gas \[B\] at the same temperature. If density of \[A=3~g/d{{m}^{3}}~\] and that of \[B=1.5~g/d{{m}^{3}}~\] and the molar mass of \[A=\dfrac{1}{2}\] of \[B\], the ratio of pressure exerted by gases is:

Answer 1

Hint:We should know the ideal gas equation in order to solve this question
-Input the values given in the question, according to the equation, keeping the unknown ratio at the left side of the equation.

Complete step by step answer:
The ideal gas law, also known as the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions, although it has several limitations. The gas law is not applicable outside the ideal given conditions. Some gases show deviation from the ideal behaviour of the gases expected from this law, when the temperature is extremely low, specifically depending on the gases. Different gases deviate in different temperatures. The equation of ideal gas law, also known as ideal gas equation can be mathematically expressed as,
$PV=nRT$
Where, $P$ is the pressure exerted by the gas, $V$ is the volume of gas under observation, $n$ symbolises the number of moles of that gas, $R$ is the gas constant and $T$ denotes the temperature in which the system is present.
We can see in the given question the temperature is the same for both the gases, i.e. the system is at constant temperature.
So, $\dfrac{P_AV_A}{P_BV_B}=\dfrac{nART}{nBRT}$
Where $P_A$ is pressure of gas \[A\], and $P_B$ pressure of gas \[B\] similarly, $nA$ and $nB$ are the number of moles of \[A\] and \[B\].
As we know, volume is mass upon density, i.e.,
$V=\dfrac{M}{D}$
Where $M$ is mass, $V$ is the volume of gas and $D$ is the density of the gas.
Using the explained logic in above ratio, we get,
$\dfrac{P_A}{P_B}=\dfrac{M_BD_A}{M_AD_B}$
Putting all the values of mass and density into the above equation, from the given question we get,
\[\dfrac{P_A}{P_B}=\dfrac{3\times \mu \beta }{1.5\times 0.5M_B}=4\]
So, the answer is the ratio of pressure of both the gases is turned out to be \[4:1\].

Note:
While approaching these questions involving finding out ratios, keep the unknown part in ratio form on the left hand side of the equation and then solve the question as it will be easier that way, and the chances of mistakes are lesser that way.