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NEET NEET Questions — Free MCQ Practice

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

A.

$3.5 cm / s$

B.

$(27 / 2) cm / s$

C.

$\sqrt{54} cm / s$

D.

$(\sqrt{54} / 2) cm / s$

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Explanation

4.

$\sqrt{\frac{(2^{2}) + (3^{2}) + (4^{2}) + (5^{2})}{4}} \sqrt{\frac{4 + 9 + 16 + 25}{4}} \sqrt{54} / 2$

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

A.

$2.5 cm \sec^{- 1}$

B.

$1.9 cm \sec^{- 1}$

C.

$3.6 cm \sec^{- 1}$

D.

$4.6 cm \sec^{- 1}$

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Explanation

3.

$\sqrt{\frac{4 \times 6^{2} + 5 + 2^{2} + 10 + 3^{2}}{19}} = \sqrt{\frac{4 + 36 + 5 + 4 + 10 + 9}{19}} = \sqrt{\frac{44 + 20 + 90}{19}} = \sqrt{\frac{254}{12}} = 3.6 cm / \sec^{- 1}$

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The ratio between the root mean square velocity of $H_{2}$ at 50 K and that of $O_{2}$ at 800 K is:

A.

4

B.

2

C.

1

D.

1/4

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If $C_{1}, C_{2}, C_{3} . . .$ represent the speeds of $n_{1}, n_{2}, n_{3} . . .$ molecules respectively, then the root mean square speed will be:

A.

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

B.

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

C.

$\sqrt{\frac{(n_{1} C_{1})}{n_{1}} + \frac{(n_{2} C_{2})}{n_{2}} + \frac{(n_{3} C_{3})}{n_{3}}}$

D.

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

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Explanation

The root mean square velocity or $v_{r m s}$ is the square root of the average square velocity and is

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The root mean square velocity of hydrogen is $\sqrt{5}$ times than that of nitrogen. If T is the temperature of the gas, then:

A.

$T_{H_{2}} = T_{N_{2}}$

B.

$T_{H_{2}} > T_{N_{2}}$

C.

$T_{H_{2}} < T_{N_{2}}$

D.

$T_{H_{2}} = \sqrt{7} T_{N_{2}}$

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Explanation

$V_{rms} = \sqrt{\frac{3 RT}{M}} = \frac{(V_{rms}) H_{2}}{(V_{rms}) N_{2}} = \sqrt{\frac{T_{H_{2}}}{M_{H_{2}}} \times \frac{M_{N_{2}}}{T_{N_{2}}};} {(V_{rms})}_{H_{2}} = \sqrt{5} {(V_{rms})}_{N_{2}} ∴ \frac{{(V_{rms})}_{H_{2}}}{{(V_{rms})}_{H_{2}}} \times \sqrt{5} = \sqrt{\frac{T_{H_{2}}}{T_{N_{2}}} \times \frac{28}{2}} = \frac{\sqrt{5}}{1} = \sqrt{\frac{T_{H_{2}}}{T_{N_{2}}} \times 14} = 5 = \frac{T_{H_{2}}}{T_{N_{2}}} \times 14 T_{N_{2}} \times 5 = T_{H_{2}} \times 14 ∴ T_{N_{2}} > T_{H_{2}}$

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

A.

259.4 K

B.

400 K

C.

532.4 K

D.

None of these

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Explanation

$Second memeber of C_{n} H_{2 n} series = C_{3} H_{6} = 42 = \sqrt{\frac{8 {RT}_{1}}{{πM}_{1}}} = \sqrt{\frac{8 {RT}_{2}}{{πM}_{2}}} = \frac{900}{71} = \frac{T_{2}}{42} T_{2} = 532.4 K$

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

A.

0.02 kg/mol

B.

0.001 kg/mol

C.

0.003 kg/mol

D.

1 kg/mol

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Explanation

$U_{rms} = \sqrt{\frac{3 RT}{M}} (or) 30 R^{\frac{1}{2}} = \sqrt{\frac{3 RT}{M}} (or) {(30)}^{2} = \frac{300 \times 3}{M} M = 1.0 g {mol}^{- 1} = 0.001 kg {mol}^{- 1} Hence answer is (d)$

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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 $N_{2}$ occupies a volume of $1 {dm}^{3}$ at 330 K and 800 atm. Calculate volume occupied by same quantity of $N_{2}$ gas at 570 K and 200 atm:

A.

1 L

B.

2 L

C.

3 L

D.

4 L

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Explanation

$Z = \frac{PV}{nRT}; 1.90 = \frac{1 \times 800}{n \times R \times 330}; n = \frac{1 \times 800}{1.90 \times R \times 330} Z = 1.10 = \frac{V \times 200}{n \times R \times 570}; 1.10 = \frac{V \times 200 \times 1.90 \times R \times 330}{800 \times R \times 570} V = 4 L$

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Consider the following statements. If the van der Waals' parameters of two gases are given as

$a / {dm}^{6} bar {mol}^{- 2} b / {dm}^{3} {mol}^{- 1} Gas A 6.5 0.055 Gas B 2 0.01$

then:

A.

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?

B.

1 and 2

C.

1, 2 and 3

D.

2 and 3

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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:

A.

$0 ° C$

B.

Its critical temperature

C.

Absolute zero

D.

Its Boyle temperature

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Explanation

1.

The volume of a fixed mass of dry gas increases or decreases by â€‹¹⁄₂₇₃ times the volume at 0 °C for every 1 °C rise or fall in temperature.

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