Question

The root mean square velocity of gas molecules at 27°c is 1365 m/s the gas is

Answer 1

Helium is the required answer.

GIVEN:

• Temperature , T = 27° C
• Root mean square of velocity, v = 1365 m/s

TO FIND:

Name of the gas

FORMULA:

Root mean square velocity, $v = \sqrt{ \frac{3RT}{M} }$

Where R is the gas constant. R = 8.314 J mol^-1 K^-1

M is the molecular mass of the gas

SOLUTION:

STEP 1: TO CONERT TEMPERATURE IN STANDARD UNITS

• SI unit of temperature is kelvin.

• °C + 273 = Kelvin

• 27 + 273 = kelvin

• Temperature in kelvin = 300 K

STEP 2: TO FIND MOLECULAR MASS OF GAS

$v = \sqrt{ \frac{3RT}{M} } \\ \\ 1365 = \sqrt{ \frac{3 \times 8.314\times 300}{M} } \\ \\ {(1365)}^{2} = \frac{900 \times 8.314}{M} \\ \\ 1863225 = \frac{7482.6}{M} \\ \\ M= \frac{7482.6}{1863225} \\ \\ M = 0.0040 \: kg \\ \\ M = 4.0 \times {10}^{ - 3} \: kg \\ \\ M = 4 \: g$

Molecular mass of the gas is 4 g

ANSWER:

Helium has the molecular mass of 4 g.

So the given gas is helium.

OTHER TYPE OF VELOCITIES:

• Root mean square velocity, v = √{3RT/M}

• Average velocity, v = √{8RT/πM}

• Most probable speed, v =√{2RT/M}

For a given gas, the magnitude of speed is: Root mean square velocity > Average velocity > Most probable speed