Free Objective Test 02 Practice Test - 11th and 12th

Question 1

If $C_{1}, C_{2}, C_{3}$ .........represent the speeds of $n_{1}, n_{2}, n_{3}$ ......... molecules, then the root mean square speed is _____.

$\frac{\sqrt{n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . .}}{n_{1} + n_{2} + n_{3} + . . .}$

$\frac{{⟮ n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . ⟯}^{\frac{1}{2}}}{n_{1} + n_{2} + n_{3} + . . . . .}$

$\frac{{⟮ n_{1} {C_{1}}^{2} ⟯}^{\frac{1}{2}}}{n_{1}} + \frac{{⟮ n_{2} {C_{2}}^{2} ⟯}^{\frac{1}{2}}}{n_{2}} + \frac{{⟮ n_{3} {C_{3}}^{2} ⟯}^{\frac{1}{2}}}{n_{3}} + . . . . .$

$⟮ \frac{{⟮ n_{1} C_{1} + n_{2} C_{2} + n_{3} C_{3} + . . . ⟯}^{2}}{⟮ n_{1} + n_{2} + n_{3} + . . . . . ⟯} ⟯^{\frac{1}{2}}$

SOLUTION

Solution : A

Root mean square speed = $\frac{\sqrt{n_{1} {C_{1}}^{2} + n_{2} {C_{2}}^{2} + n_{3} {C_{3}}^{2} + . . .}}{n_{1} + n_{2} + n_{3} + . . .}$

Question 2

The ratio of the rate of diffusion of helium and methane under identical condition of pressure and temperature will be___.

0.5

SOLUTION

Solution : B

$\frac{r_{H e}}{r_{C H_{4}}} = \sqrt{\frac{M_{C H_{4}}}{M_{H e}}} \Rightarrow \sqrt{(} \frac{16}{4}) \Rightarrow 2$

Question 3

In which of the gases given below, the average speed of the molecule is the least at 1000K?

$C O_{2}$

$S O_{2}$

$O_{2}$

$C H_{4}$

SOLUTION

Solution : B

Speed is inversely proportional to molecular weight. Molecular weight of $S O_{2}$ is highest among the four. Hence its speed is least.

Question 4

The temperature and pressure at which ice, liquid water and water vapour can exist together are

0 $^{\circ}$ C, 1atm

2 $^{\circ}$ C, 4.7atm

C. 0

^{\circ}

C, 4.7mm

D. 2

^{\circ}

C, 4.7mm

SOLUTION

Solution : C

All the three phases of water can coexist at 0 $^{\circ}$ C & 4.7 mm pressure.

Question 5

Helium atom is two times heavier than a hydrogen molecule at 298 K, the average kinetic energy of helium is

Two times that of a hydrogen molecule

Same as that of a hydrogen molecule

Four times that of a hydrogen molecule

Half that of a hydrogen molecule

SOLUTION

Solution : B

$\frac{E_{H e}}{E_{H_{2}}} = \sqrt{\frac{T_{H_{e}}}{T_{H_{2}}}}$ so energies will be same for

He & $H_{2}$ at same temperature.

Question 6

The temperature at which RMS velocity of $S O_{2}$ molecules is half that of He molecules at 300 K is

150 K

600 K

900 K

1200 K

SOLUTION

Solution : D

$\frac{U_{S O_{2}}}{U_{H} e} = \frac{1}{2} = \sqrt{\frac{M_{H e}}{M_{S O_{2}}} \frac{T_{S O_{2}}}{T_{H e}}} = \sqrt{\frac{4}{64} \frac{T_{S O_{2}}}{300}}$

$= \frac{4}{64} \frac{T_{S O_{2}}}{300} = \frac{1}{4}; T_{S O_{2}} = 1200^{\circ} K$

Question 7

The compressibility factor of a gas is less than 1 at STP. Its molar volume Vm will be

Vm > 22.42

Vm < 22.42

Vm = 22.42

None

SOLUTION

Solution : B

If Z<1 then molar volume is less than 22.4 L

Question 8

$n_{1}$ and $n_{2}$ moles of two ideal gases (mol. wt. $M_{1}$ and $M_{2}$ ) respectively at temperature $T_{1}$ K and $T_{2}$ K are mixed. Assuming that no loss of energy, the temperature of mixture becomes -

$n_{1} T_{1} + n_{2} T_{2}$

$\frac{n_{1} T_{1} + n_{2} T_{2}}{T_{1} + T_{2}}$

$\frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}}$

$\frac{n_{1} \times T_{2}}{n_{1} \times n_{2}}$

SOLUTION

Solution : C

Let the final temperature be T , then K $E_{1}$ + K $E_{m i x t u r e}$

$\frac{3}{2}$ $n_{1} R T_{1}$ + $\frac{3}{2}$ $n_{2} R T_{2}$ = $\frac{3}{2}$ ( $n_{1} + n_{2}$ ) RT

T = $\frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}}$

Question 9

A cubical vessel has a side with 'I' cm lenth contained a gas at a pressure of 'p'. when the side of the vessel is made $\frac{1}{2}$ cm, the pressure of gas becomes?

$\frac{P}{8}$

SOLUTION

Solution : D

$P_{1}$ $V_{1}$ = $P_{2}$ $V_{2}$

P. $l^{3}$ = $p_{2}$ ${(\frac{1}{2})}^{3}$

$P_{2}$ = 8P

Question 10

At what temperature, the volume of 'V' of a certain mass of a gas at $37^{o} C$ will be doubled, keeping the pressure constant?

$327^{o} C$

$347^{o} C$

$527^{o} C$

$54^{o} C$

SOLUTION

Solution : B

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$
$V_{1} = V, T_{1} = 37 + 273 = 310 k$
$V_{2} = 2 V, T_{2} = ?$
$\frac{V}{310} = \frac{2 V}{T_{2}}$
$T_{2} = 620 K = 347^{o} C$

Question 11

Pressure of a mixture of 4 g of O₂ and 2 g of H₂ confined in a bulb of 1 litre at 0°C is___.

25.215 atm

31.205 atm

45.215 atm

15.210 atm

SOLUTION

Solution : A

No. of moles of $O_{2} = \frac{4}{32} = 0.125$

No.of moles of $H_{2} = \frac{2}{2} = 1$

Total no. of moles = 1+0.125 = 1.125

$P = \frac{n R T}{V} = \frac{1.125 \times 0.082 \times 273}{1} = 25.215 a t m$

Question 12

For one mole of a van der Waal's gas when b =o and T = 300 K, the PV vs $\frac{1}{V}$ plot is shown below. The value of the Van der Waal's constant "a" ( $a t m L^{2} m o l^{- 2}$ ) is

1.0

4.5

1.5

3.0

SOLUTION

Solution : C

$⟮ P + \frac{a}{V^{2}} ⟯ ⟮ V ⟯ = R T$

PV + $\frac{a}{V}$ = RT

y = RT –a(V)

y = RT –a(x)

So, slope = a = $\frac{21.6 - 20.1}{3 - 2} = \frac{1.5}{1} = 1.5$

Question 13

The density of vapour of a substance (X) at 1 atm pressure and 500 K is 0.8 $\frac{k g}{m^{3}}$ . The vapour effuses through a small hole at a rate of $\frac{4}{5}$ times slower than oxygen under the same condition. What is the compressibility factor (Z) of the vapour?

0.974

1.35

1.52

1.22

SOLUTION

Solution : C

$\frac{r_{x}}{r_{O_{2}}} = \sqrt{\frac{M_{O_{2}}}{M_{x}}} = ⟮ \frac{4}{5} ⟯^{2} = \frac{32}{M_{x}} \Rightarrow M_{x} = 50$

$d_{x} = 0.80 k g m^{- 3}$

$V_{m} = \frac{1000}{800} \times 50 = 62.5 L$

$Z = \frac{P V_{m}}{R T} = \frac{1 \times 62.5}{0.0821 \times 500} = 1.52$

Question 14

The temperature above which gas cannot be liquefied by application of pressure alone is

Boyle temperature

Curie temperature

Critical temperature

None of the above

SOLUTION

Solution : C

This is the definition of critical temperature.

Question 15

The density of Ne is maximum at

$S T P$

$0^{\circ} C, 2 a t m$

$273^{\circ} C, 1 a t m$

$273^{\circ} C, 2 a t m$

SOLUTION

Solution : B

For an ideal gas, density(d) will be the maximum when Pressure is high and the temperature is low.

$d = \frac{P M}{R T} (o r) d \propto \frac{P}{T}$

Therefore option B is correct as it satisfies these conditions.

Free Objective Test 02 Practice Test - 11th and 12th

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

Question 11

SOLUTION

Question 12

SOLUTION

Question 13

SOLUTION

Question 14

SOLUTION

Question 15

SOLUTION

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