States of Matter

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

In thermodynamics, the $P-V$ work done is given by

$$w = -\int dV\,P_{\text{ext}}.$$

For a system undergoing a particular process, the work done is,

$$w = -\int dV\left(\frac{RT}{V-b} - \frac{a}{V^2}\right).$$

This equation is applicable to a

Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulfuric acid are combined for the reaction?

(Use molar mass of aluminium as $27.0\ \mathrm{g\,mol^{-1}}$, $R = 0.082\ \mathrm{atm\,L\,mol^{-1}\,K^{-1}}$)

Which of the following statement(s) is(are) correct regarding the root mean square speed $(u_{rms})$ and average translational kinetic energy $(\varepsilon_{av})$ of a molecule in a gas at equilibrium?

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m³) of the compartment A after the system attains equilibrium is ______.

Among the following, the incorrect statement is :

At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen ($\ce{N2}$) at 4 bar. The molar mass of gaseous molecule is :

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_i$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$. The final pressure $p_f$ is :

At very high pressures, the compressibility factor of one mole of a gas is given by :

Which intermolecular force is most responsible in allowing xenon gas to liquefy ?

Initially, the root mean square (rms) velocity of $\ce{N2}$ molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

One mole of a monoatomic real gas satisfies the equation $p(V-b)=RT$ where $b$ is a constant. The relationship of interatomic potential $V(r)$ and interatomic distance $r$ for the gas is given by

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is :

Which of the following is not an assumption of the kinetic theory of gases ?

When does a gas deviate the most from its ideal behaviour ?

The value of d in cm (shown in the figure), as estimated from Graham's law, is

The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to

If Z is a compressibility factor, van der Waals equation at low pressure can be written as :

Van der Waal's equation for a gas is stated as,
$$p=\frac{nRT}{V-nb}-a\left(\frac nV\right)^2.$$
This equation reduces to the perfect gas equation, $p=\dfrac{nRT}{V}$ when ,