Which of the following statement(s) are correct:

(1) A plot of log KP versus 1/T is linear

(2) A plot of log (X) versus time is linear for a first-order reaction $\mathrm{X}\to \mathrm{P}$'

(3) A plot of log P versus 1/T is linear at constant volume

(4) A plot of P versus 1/V is linear at a constant temperature.

(1) 1, 2

(2) 2, 4

(3) 2, 3

(4) 1, 4

The ratio of root mean square velocity to the average velocity of a gas molecule at a particular temperature is

(1) 1:1.086

(2) 2:1.086

(3) 1.086:1

(4) 1.086:2

An L.P.G. cylinder contains 15 kg of butane gas at $27°\mathrm{C}$ and 10 atmospheric pressure, It was leaking and its pressure fell down to 8 atmospheric pressure after one day. The gas leaked in 5 days is

(1) 10 kg

(2) 3 kg

(3) 15 kg

(4) 12 kg

The partial pressure of oxygen in a flask containing 16 g ${\mathrm{O}}_2$ and 32 g ${\mathrm{SO}}_2$ is-

1. 1/16 of total pressure

2. 1/2 of total pressure

3. 2/3 of total pressure

4. None of the above

The most probable speeds of the molecules of gas A at ${\mathrm{T}}_1\mathrm{K}$ and gas B at ${\mathrm{T}}_2\mathrm{K}$ are in the ratio 0.715:1. The same ratio for gas A at ${\mathrm{T}}_2\mathrm{K}$ and gas B ${\mathrm{T}}_1\mathrm{K}$ is 0.954. Find the ratio of molar masses ${\mathrm{M}}_{\mathrm{A}}:{\mathrm{M}}_{\mathrm{B}}.$

(1) 1.965

(2) 1.0666

(3) 1.987

(4) 1.466

A 200 mL flask having oxygen at 220 mm and a 300 mL flask having nitrogen at 100 mm are connected in such a way that ${\mathrm{O}}_2 \mathrm{and} {\mathrm{N}}_2$ may combine in their volumes if temperature is kept constant. The total pressure of the gaseous mixture is-

1. 158 mm

2. 138 mm

3. 148 mm

4. 168 mm

Given below is the graphical representation of volumes occupied by several gases at STP  at Y axis and mass at X axis. find out which gas/gases is/are not placed at the correct position?

1. He, NH₃ 

2. CH₄, He

3. NH₃, H₂ 

4. NH₃, CH₄ 

The compressibility factor of a gas is less than unity at STP. The correct statement among the following is -

1. ${\mathrm{V}}_{\mathrm{m}}$  > 22.4 L

2. ${\mathrm{V}}_{\mathrm{m}}$ < 22.4 L

3. ${\mathrm{V}}_{\mathrm{m}}$ = 22.4 L

4. ${\mathrm{V}}_{\mathrm{m}}$ = 44.8 L

At $100°C$ and 1 atm, if the density of liquid water is 1.0 g $c{m}^{-3}$ and that of water vapour is 0.0006 g $c{m}^{-3}$, then the volume occupied by water molecules is 1 litre of steam at that temperature

1. 6 $C{M}^3$

2. 60 $C{M}^3$

3. 0.6 $C{M}^3$

4. 0.06 $C{M}^3$

The root mean square velocity of one mole of a monoatomic gas having molar mass M is $u_{rm{s}^{}}$.

The relation between the average kinetic energy (E) of the gas and $u_{rm{s}^{}}$is

1. $U_{rms}=\surd (3E/2M)$

2. $U_{rms}=\surd (2E/3M)$

3. $U_{rms}=\surd (2E/M)$

4. $U_{rms}=\surd (E/3M)$