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

A mixture of Ne and Ar at 250 K has a total K.E.=3 kJ in a closed vessel, the total mass if Ne and Ar is 30 g. Find mass % of Ne in a gaseous mixture at 250 K.

1.  61.63 %

2.  38.37 %

3.  50 %

4.  28.3 %

In two vessels of 1 litre each at the same temperature 1 g of ${\mathrm{H}}_2$ and 1 g of ${\mathrm{CH}}_4$ are taken, for these:

1.  ${\mathrm{V}}_{\mathrm{rms}}$ values will be same

2.  Kinetic energy per mol will be same

3.  Total kinetic energy will be same

4.  Pressure will be same

Four particles have speed 2, 3, 4 and 5 cm/s respectively. Their rms speed is:

1.  $3.5 \mathrm{cm}/\mathrm{s}$

2.  $\left(27/2\right) \mathrm{cm}/\mathrm{s}$

3.  $\sqrt{54} \mathrm{cm}/\mathrm{s}$

4.  $\left(\sqrt{54}/2\right) \mathrm{cm}/\mathrm{s}$

A gaseous mixture contains 4 molecules with a velocity of $6 \mathrm{cm} {\sec }^{-1}$, 5 molecules with a velocity of $2 \mathrm{cm} {\sec }^{-1}$ and 10 molecules with a velocity of $3 \mathrm{cm} {\sec }^{-1}$. What is the RMS velocity of the gas:

1.  $2.5 \mathrm{cm} {\sec }^{-1}$

2.  $1.9 \mathrm{cm} {\sec }^{-1}$

3.  $3.6 \mathrm{cm} {\sec }^{-1}$

4.  $4.6 \mathrm{cm} {\sec }^{-1}$

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.  $\sqrt{\frac{{\left({\mathrm{n}}_1{\mathrm{C}}_1+{\mathrm{n}}_2{\mathrm{C}}_2+{\mathrm{n}}_2{\mathrm{C}}_3 +...\right)}^2}{{\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3 +...}}$

At what temperature will average speed of the molecules of the second member of the series ${\mathrm{C}}_{\mathrm{n}}{\mathrm{H}}_{2\mathrm{n}}$ be the same of ${\mathrm{Cl}}_2$ at $627°\mathrm{C}$?

1.  259.4 K

2.  400 K

3.  532.4 K

4.  None of these

If ${\mathrm{U}}_{\mathrm{RMS}}$ of a gas is $30 {\mathrm{R}}^{1/2} {\mathrm{ms}}^{-1} \mathrm{at} 27°\mathrm{C}$ then the molar mass of gas is:

1.  0.02 kg/mol

2.  0.001 kg/mol

3.  0.003 kg/mol

4.  1 kg/mol

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