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The mean free path ($\mathrm{\lambda }$) of a gas sample is given by:
1. $\lambda =\sqrt{2}\pi {\sigma }^{2}N$                               
2. $\lambda =1/\sqrt{2}\pi {\sigma }^{2}N$
3. $\lambda =\sqrt{2}\pi \mu {\sigma }^{2}N$                               
4. none of these

Joule-Thomson coefficient ($\partial \mathrm{T}/\partial \mathrm{P}$)_H for an ideal gas is:
1. zero                                 
2. +ve
3. -ve                                   
4. none of these

At high pressure, the compressibility factor 'Z' is equal to- 
1. Unity
2. 1-$\frac{\mathrm{Pb}}{\mathrm{RT}}$
3. 1+$\frac{\mathrm{Pb}}{\mathrm{RT}}$
4. Zero

A sample of water gas has a composition by volume of 50% H₂, 45% CO and 5% CO₂. Calculate the volume in litre at S.T.P. of water gas which on treatment with excess of stream will produce 5 litre H₂. The equation for the reaction is : CO + H₂O $\stackrel{}{\to }$ CO₂+ H₂
(1) 4.263 Litre
(2) 5.263 Litre
(3) 6.263 Litre
(4) 7.263 Litre

Flask A of volume 10 litre containing 20 gram of H₂ and flask B of volume 10 litre containing 88 gram CO₂ are connected by a connector having negligible volume. When the valve of the connector is opened, the composition of H₂ gas in flask B after opening the valve is-
   
1. 10%
2. 13%
3. 15%
4. 20%

If the average velocity of N₂ molecules is 0.3 m/s at 27°C, then the velocity of 0.6 m/s will take place at 
(1) 273 K
(2) 927 K
(3) 1000 K
(4) 1200 K

What volume of oxygen gas (O₂) measured at 0°C and 1 atm, is needed to burn completely 1 L of propane gas (C₃H₈) measured under the same conditions?
(1) 7L
(2) 6L
(3) 5L
(4) 10L

The mean free path of gas A, with molecular diameter equal to 4 Å, contained in a vessel, at a pressure of ${10}^{–6}$ torr, is 6990 cm. The vessel is evacuated and then filled with gas B, with molecular diameter, equal to 2 Å, at a pressure of ${10}^{–3}$ torr, the temperature remaining the same. The mean free path of gas B will be
(A) 28 cm                       
(B) 280 cm
(C) 7 cm                         
(D) 14 cm

Two vessels of capacities 3 litres and 4 litres are separately filled with a gas. The pressures are respectively 202 kPa and 101 kPa. The two vessels are connected. The gas pressure will be now, at constant temperature.
(1) 151.5 kPa                             
(2) 144 kPa
(3) 303 kPa                                 
(4) 175 kPa

The pressure in bulb dropped from 2000 to 1500 mm Hg in 47 mins. when the ${\mathrm{O}}_2$ present in the bulb leaked through a small hole. The bulb was then completely evacuated. A mixture of ${\mathrm{O}}_2$ and another gas of molecular weight of 79 in the molar ratio 1 : 1 at a total pressure of 4000 mm Hg was introduced. Find the mole ratio of two gases remaining in the bulb after a period of 74 mins.
(A) 1 : 1.236                       
(B) 1 : 2.136
(C) 1 : 3.336                       
(D) 2 : 1.136

Which of the following curve does not represent Boyle's law?
1.     
2.
3.
4.

A certain hydrate has the formula ${\mathrm{MgSO}}_4.$ ${\mathrm{xH}}_2\mathrm{O}$. A quantity of 54.2 g of the compound is heated in an oven to drive off the water. If the water vapour generated exerts a pressure of 24.8 atm in a 2.0 L container at 120$°\mathrm{C}$, the value of x is-
1.  2
2.  5
3.  6
4.  7

The ratio between the root mean square velocity of ${\mathrm{H}}_2$ at 50 K and that of ${\mathrm{O}}_2$ at 800 K is:
1.  4
2.  2
3.  1
4.  1/4

If ${\mathrm{C}}_1, {\mathrm{C}}_2, {\mathrm{C}}_3...$ represent the speeds of ${\mathrm{n}}_1, {\mathrm{n}}_2, {\mathrm{n}}_3...$ molecules respectively, then the root mean square speed will be:
1.  $\sqrt{\frac{{\mathrm{n}}_1{\mathrm{C}}_1^2+{\mathrm{n}}_2{\mathrm{C}}_2^2+{\mathrm{n}}_3{\mathrm{C}}_3^2 +...}{{\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3 +...}}$
2.  $\sqrt{\frac{{\left({\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3 +...\right)}^2}{{\mathrm{n}}_1{\mathrm{C}}_1^2+{\mathrm{n}}_2{\mathrm{C}}_2^2+{\mathrm{n}}_3{\mathrm{C}}_3^2 +...}}$
3.  $\sqrt{\frac{\left({\mathrm{n}}_1{\mathrm{C}}_1\right)}{{\mathrm{n}}_1}+\frac{{\displaystyle \left({\mathrm{n}}_2{\mathrm{C}}_2\right)}}{{\displaystyle {\mathrm{n}}_2}}+\frac{{\displaystyle \left({\mathrm{n}}_3{\mathrm{C}}_3\right)}}{{\displaystyle {\mathrm{n}}_3}}}$
4.  $\sqrt{\frac{{\left({\mathrm{n}}_1{\mathrm{C}}_1+{\mathrm{n}}_2{\mathrm{C}}_2+{\mathrm{n}}_2{\mathrm{C}}_3 +...\right)}^2}{{\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3 +...}}$

Consider the following statements. If the van der Waals' parameters of two gases are given as
$\mathrm{a}/{\mathrm{dm}}^6 \mathrm{bar} {\mathrm{mol}}^{-2} \mathrm{b}/{\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$
$\mathrm{Gas} \mathrm{A} 6.5 0.055$
$\mathrm{Gas} \mathrm{B} 2 0.01$
then:
1.  Critical volume of A > Critical volume of B
2.  Critical pressure A > Critical temperature of B
3.  Critical temperature of A > Critical temperature of B
Which of the above statement is incorrect?
1.  1 alone
2.  1 and 2
3.  1, 2 and 3
4.  2 and 3

Pressure remaining the same, the volume of a given mass of an ideal gas increase for every degree centigrade rise in temperature by definite fraction of its volume at:
1.  $0°\mathrm{C}$
2.  Its critical temperature
3.  Absolute zero
4.  Its Boyle temperature

Two flasks A and B of equal volume containing ${\mathrm{NH}}_3$ and HCl gases, are connected by a narrow tube of negligible volume. The two gases were prevented from mixing by stopper fitted in connecting tube. For further detail of experiment refer to the given figure. What will be final pressure in each flask when passage connecting two tubes are opened. Assume ideal gas behaviour of ${\mathrm{NH}}_3$ and $\mathrm{HCl}$ gas and the reaction.
     
(1) 40 mm Hg                                         
(2) 60 mm Hg
(3) 20 mm Hg                                         
(4) 10 mm Hg

Two flasks of equal volume are connected by a narrow tube (of negligible volume) at 27ºC and contain 0.70 mole of ${\mathrm{H}}_2$ at 0.5 atm. One of the flasks is then immersed in a hot bath, kept at 127 ºC, while the other remains at 27 ºC. The final pressure is -
1. 5.714 atm                   
2. 0.5714 atm
3. 2.5214 atm                 
4. 5.5114 atm

Which is not correct curve for gay-lusacc's law?
1 .
2.     
3.   
4.     
 

The compressibility factor for nitrogen at 330 K and 800 atm is 1.90 and at 570 K and 200 atm is 1.10. A certain mass of ${\mathrm{N}}_2$ occupies a volume of $1 {\mathrm{dm}}^3$ at 330 K and 800 atm. Calculate volume occupied by same quantity of ${\mathrm{N}}_2$ gas at 570 K and 200 atm:
1.  1 L
2.  2 L
3.  3 L
4.  4 L

The van der Waal's equation of law of corresponding states for 1 mole of gas is:
1.  $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^2}\right) \left(3{\mathrm{V}}_{\mathrm{r}}-1\right)=8{\mathrm{T}}_{\mathrm{r}}$
2.  $\left({\mathrm{P}}_{\mathrm{r}}-\frac{3}{{\mathrm{V}}_{\mathrm{r}}^2}\right) \left(3{\mathrm{V}}_{\mathrm{r}}-1\right)=8{\mathrm{T}}_{\mathrm{r}}$
3.  $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^2}\right) \left(3{\mathrm{V}}_{\mathrm{r}}+1\right)=8{\mathrm{\pi T}}_{\mathrm{r}}$
4.  $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^2}\right) \left(3{\mathrm{V}}_{\mathrm{r}}+1\right)=8$