Chapter 5

Rate of diffusion of a gas is: (a) directly proportional to its density. (b) directly proportional to its molecular weight. (c) directly proportional to the square root of its molecular weight. (d) inversely proportional to the square root of its molecular weight.

Using van der Waal's equation, calculate the constant, ' \(a\) ' when two moles of a gas confined in a four litre flask exerts a pressure of \(11.0\) atmospheres at a temperature of \(300 \mathrm{~K}\). The value of ' \(b\) ' is \(0.05 \mathrm{~L}\) mol

Equal weights of methane and hydrogen are mixed in an empty container at \(25^{\circ} \mathrm{C}\). The fraction of the total pressure exerted by hydrogen is : (a) \(\frac{1}{2}\) (b) \(\frac{8}{9}\) (c) \(\frac{1}{9}\) (d) \(\frac{16}{17}\)

Equal weights of methane and oxygen are mixed in an empty container at \(25^{\circ} \mathrm{C}\). The fraction of the total pressure exerted by oxygen is (a) \(\frac{1}{3}\) (b) \(\frac{1}{2}\) (c) \(\frac{2}{3}\) (d) \(\frac{1}{3} \times \frac{273}{298}\)

According to kinetic theory of gases [2011] (a) collisions are always elastic (b) heavier molecules transfer more momentum to the wall of the container (c) only a small number of molecules have very high velocity (d) between collisions, the molecules move in straight lines with constant

The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is (a) Critical temperature (b) Boyle temperature (c) Inversion temperature (d) Reduced temperature

Read the following statement and explanation and answer as per the options given below : Assertion : The pressure of a fixed amount of an ideal gas is proportional to its temperature Reason : Frequency of collisions and their impact both increase in proportion to the square root of temperature. (a) If both assertion and reason are CORRECT, and reason is the CORRECT explanation of the assertion. (b) If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion. (c) If assertion is CORRECT, but reason is INCORRECT. (d) If assertion is INCORRECT, but reason is CORRECT.

A gas bulb of 1 litre capacity contains \(2.0 \times 10^{21}\) molecules of nitrogen exerting a pressure of \(7.57 \times 10^{3} \mathrm{Nm}^{-2} .\) Calculate the root mean square (r.m.s) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square speed is \(0.82\), calculate the most probable speed for these molecules at this temperature.

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 ____ .

The degree of dissociation is \(0.4\) at \(400 \mathrm{~K}\) and \(1.0 \mathrm{~atm}\) for the gaseous reaction \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\). Assuming ideal behaviour of all gases, calculate the density of equilibrium mixture at \(400 \mathrm{~K}\) and \(1.0\) atmosphere. (Relative atomic mass of \(\mathrm{P}=31.0\) and \(\mathrm{Cl}=35.5\) ) \([1998-3\)

For the reaction, \(\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})+0.5 \mathrm{O}_{2}(\mathrm{~g})\), calculate the mole fraction of \(\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g})\) decomposed at a constant volume and temperature, if the initial pressure is \(600 \mathrm{~mm} \mathrm{Hg}\) and the pressure at any time is 960 \(\mathrm{mm}\) Hg. Assume ideal gas behaviour.

At room temperature, ammonia gas at 1 atm pressure and hydrogen chloride gas at \(P\) atm pressure are allowed to effuse through identical pin holes from opposite ends of a glass tube of one metre length and of uniform cross- section. Ammonium chloride is first formed at a distance of \(60 \mathrm{~cm}\) from the end through which HCl gas is sent in. What is the value of \(P\) ?

A straight glass tube has two inlets \(X\) and \(Y\) at two ends. The length of tube is \(200 \mathrm{~cm} . \mathrm{HCl}\) gas through inlets \(X\) and \(\mathrm{NH}_{3}\) gas through inlet \(Y\) are allowed to enter the tube at the same time. What fumes appear at point \(P\) inside the tube. Find distance of \(P\) from \(X\).

Calculate density of \(\mathrm{NH}_{3}\) at \(30{ }^{\circ} \mathrm{C}\) and 5 atm pressure.

The value of \(P V\) for \(5.6\) litres of an ideal gas is \(\ldots \ldots \ldots \ldots \ldots . R T\), at N.T.P.

If a gas is expanded at constant temperature : (a) the pressure decreases (b) the kinetic energy of the molecules remains the same (c) the kinetic energy of the molecules decreases (d) the number of molecules of the gas increases

When an ideal gas undergoes unrestrained expansion, no cooling occurs because the molecules : (a) are above the inversion temperature (b) exert no attractive forces on each other (c) do work equal to loss in kinetic energy (d) collide without loss of energy

Match the type of interaction in column A with the distance dependence of their interaction energy in column B : A \(\quad\) B (I) ion-ion (A) \(\frac{1}{\mathrm{r}}\) (II) dipole-dipole (B) \(\frac{1}{\mathrm{r}^{2}}\) (III) London dispersion (C) \(\frac{1}{\mathrm{r}^{3}}\) (D) \(\frac{1}{\mathrm{r}^{6}}\) (a) \((\mathrm{I})-(\mathrm{B}),(\mathrm{II})-(\mathrm{D}),(\mathrm{III})-(\mathrm{C})\) (b) \((\mathrm{I})-(\mathrm{A}),(\mathrm{II})-(\mathrm{B}),(\mathrm{III})-(\mathrm{D})\) (c) (I)-(A), (II)-(B), (III)-(C) (d) (I)-(A), (II)-(C), (III)-(D)

One mole of nitrogen gas at \(0.8\) atm takes \(38 \mathrm{~s}\) to diffuse through a pinhole, whereas one mole of an unknown compound of xenon with flourine at \(1.6\) atm takes \(57 \mathrm{~s}\) to diffuse through the same hole. Calculate the molecular formula of the compound.

The pressure exerted by \(12 \mathrm{~g}\) of an ideal gas at temperature \(t^{\circ} \mathrm{C}\) in a vessel of volume \(V\) litre is one atm. When the temperature is increased by 10 degrees at the same volume, the pressure increases by \(10 \%\). Calculate the temperature \(t\) and volume \(V\). (Molecular weight of the gas \(=120\).)

An evacuated glass vessel weighs \(50.0 \mathrm{~g}\) when empty, \(148.0 \mathrm{~g}\) when filled with a liquid of density \(0.98 \mathrm{~g} \mathrm{~mL}^{-1}\) and \(50.5 \mathrm{~g}\) when filled with an ideal gas at \(760 \mathrm{~mm} \mathrm{Hg}\) at \(300 \mathrm{~K}\). Determine the molar mass of the gas.

A mixture of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) and ethene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) occupies 40 litres at \(1.00\) atm and at \(400 \mathrm{~K}\). The mixture reacts completely with \(130 \mathrm{~g}\) of \(\mathrm{O}_{2}\) to produce \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). Assuming ideal gas behaviour, calculate the mole fractions of \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\) in the mixture.

The composition of the equilibrium mixture ( \(\mathrm{Cl}_{2} \rightleftharpoons 2 \mathrm{Cl}\) ), which is attained at \(1200^{\circ} \mathrm{C}\), is determined by measuring the rate of effusion through a pin- hole. It is observed that at \(1.80 \mathrm{mmHg}\) pressure, the mixture effuses \(1.16\) times as fast as krypton effuses under the same conditions. Calculate the fraction of the chlorine molecules dissociated into atoms. (Relative atomic mass of \(\mathrm{Kr}=84\).)

A \(20.0 \mathrm{~cm}^{3}\) mixture of \(\mathrm{CO}, \mathrm{CH}_{4}\) and He gases is exploded by an electric discharge at room temperature with excess of oxygen. The volume contraction is found to be \(13.0 \mathrm{~cm}^{3}\). A further contraction of \(14.0 \mathrm{~cm}^{3}\) occurs when the residual gas is treated with KOH solution. Find out the composition of the gaseous mixture in terms of volume percentage.

A 4 : 1 molar mixture of \(\mathrm{He}\) and \(\mathrm{CH}_{4}\) is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. What is the composition of the mixture effusing out initially?

At room temperature the following reactions proceed nearly to completion : $$ 2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2} \rightarrow \mathrm{N}_{2} \mathrm{O}_{4} $$ The dimer, \(\mathrm{N}_{2} \mathrm{O}_{4}\), solidifies at \(262 \mathrm{~K}\). A \(250 \mathrm{~mL}\) flask and a \(100 \mathrm{~mL}\). flask are separated by a stop-cock. At \(300 \mathrm{~K}\), the nitric oxide in the larger flask exerts a pressure of \(1.053 \mathrm{~atm}\). and the smaller one contains oxygen at \(0.789\) atm. The gases are mixed by opening the stopcock and after the end of the reaction the flasks are cooled at \(220 \mathrm{~K}\). Neglecting the vapour pressure of the dimer, find out the pressure and composition of the gas remaining at \(220 \mathrm{~K}\). (Assume the gases to behave ideally).

Calculate the volume occupied by \(5.0 \mathrm{~g}\) of acetylene gas at \(50^{\circ} \mathrm{C}\) and \(740 \mathrm{~mm}\) pressure.

A spherical balloon of \(21 \mathrm{~cm}\) diameter is to be filled up with hydrogen at N.T.P. from a cylinder containing the gas at 20 atmospheres at \(27^{\circ} \mathrm{C}\). If the cylinder can hold \(2.82\) litres of water, calculate the number of balloons that can be filled up.

Oxygen is present in 1 litre flask at a pressure of \(7.6 \times 10^{-10} \mathrm{~mm}\) of \(\mathrm{Hg}\). Calculate the number of oxygen molecules in the flask at \(0^{\circ} \mathrm{C}\).

When \(2 \mathrm{~g}\) of a gas \(A\) is introduced into an evaluated flask kept at \(25^{\circ} \mathrm{C}\), the pressure is found to be one atmosphere. If \(3 \mathrm{~g}\) of another gas \(B\) is then added to the same flask, the total pressure becomes \(1.5\) atm. Assuming ideal gas behaviour, calculate the ratio of the molecular weights \(M_{A}: M_{B}\)

1 litre of mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) is taken. The mixture is passed through a tube containing red hot charcoal. The volume now becomes 1.6 litre. The volumes are measured under the same conditions. Find the composition of mixture by volume.

\(3.7 \mathrm{~g}\) of a gas at \(25^{\circ} \mathrm{C}\) occupied the same volume as \(0.184 \mathrm{~g}\) of hydrogen at \(17^{\circ} \mathrm{C}\) and at the same pressure. What is the molecular weight of the gas?