Question

The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A. What will be the ratio of the pressures acting on B and A ?
A. $1/4$
B. $7/8$
C. $2/5$
D. $1/6$

Answer 1

Hint: The ideal gas law which is also known as the general gas equation as it is commonly used for the gas. It is the equation of state of an imaginary ideal gas. It is a good approximation or good guess of the behavior of many gases under many different conditions. However it has several limitations.

Formula Used: $d/p$=$M/RT$

Complete step by step solution:
According to ideal gas equation-
                            $d/p$=$M/RT$
 Let the density of gas B be as $d$.
    ∴ density of gas $A = 3d$.
and the molecular weight of A be $M$.

∴ molecular weight of $B = 2M$.
Since, $R$ is gas constant and $T$ is same for both gases, so
    $PA = dART$ and $PB = dBRT/MB$
So solving the above equations,
$PB/PA = dB/DA \times MA/MB$
$d/3d \times M/2M = 1/6$

So, the correct answer is D.

Additional information:
The equation of empire given here relates to the simplest of a really perfect ideal gas or an estimate to an actual gasoline that behaves like an ideal fuel. There are in fact many unique styles of the equation of a country. However the proper fuel law neglects both the molecular size and intermolecular sights but it's far most correct for monatomic gases which are at high temperatures and low pressures. For large volumes at the decreasing pressures, because the average distance between adjacent molecules becomes too larger than the molecular length. The relative significance of intermolecular sights reduces with increasing thermal kinetic energy and with increasing temperatures. More targeted equations of empire, consisting of the van der Waals equation, description for deviations from ideality resulting from molecular length and intermolecular forces.

Note: The state of an amount of gas is checked by its pressure, volume, and temperature. The modern form of the equation narrates these basically in two main forms. The temperature used in the equation of state is an absolute temperature and the appropriate SI unit is the kelvin.