Chemistry, asked by madhuramnuthan, 9 months ago

98 The RMS velocity of a gas at 0°C is 2m/s. The
RMS velocity of the same gas at 819°C​

Answers

Answered by Anonymous
0

Given - Vrms 1 = 2 m/s

Temperature 1 - 0° C

Temperature 2 - 819° C

Find - Vrms 2

Solution - Root mean square velocity of a gas is calculated by the formula -

Vrms = ✓(3RT/M). In the formula, R is gas constant, T is temperature in Kelvin and M is mass of gas.

The question considers velocity and temperature of same gas. Hence, mass and gas constant being same will be cancelled.

Temperature 1 - 373 K

Temperature 2 - 1092 K

Keeping the values in equation-

2/ Vrms 2 = ✓(373/1092)

2/ Vrms 2 = ✓0.34

2/ Vrms 2 = 0.584

Vrms 2 = 3.42 m/s

Hence, Root mean square velocity of gas at temperature 819 °C is 3.42 m/s

Answered by Mysterioushine
7

GIVEN :-

  • RMS velocity of a gas at 0°C is 2m/s

TO FIND :-

  • RMS velocity of the same gas at 819°C

SOLUTION :-

We have ,

T₁ = 0°C = 273K

T₂ = 819°C = 273 + 819 = 1092K

r₁ = 2m/s

r₂ = x (let)

Ratio of RMS velocities of same gas at two different temperatures is given by,

 \large  {\underline{\bold {\boxed {\bigstar{ \:  \:   \dfrac{r_{1}}{r_{2}} =  \sqrt{ \dfrac{T_{1}}{ T_{2}} } }}}}}

Where ,

  • r₁ is RMS velocity of the gas at temperature T₁
  • r₂ is RMS velocity of the gas at temperature T₂

\large{\implies{\sf{\frac{2}{x}=\sqrt{\frac{273}{1092}}}}}

\large{\implies{\sf{\frac{2}{x}=\sqrt{\frac{\cancel{273}}{\cancel{1092}}}}}}

\large{\implies{\sf{\frac{2}{x}\:=\sqrt{0.25}}}}

\large{\implies{\sf{\frac{2}{x}=\sqrt{(0.5)^2}}}}

\large{\implies{\sf{\frac{2}{x}=0.5}}}

\large{\implies{\sf{x\times\:0.5\:=\:2}}}

\large{\implies{\sf{x\:=\:\frac{2}{0.5}}}}

\large{\implies{\sf{x\:=\:\frac{2\times\:10}{5}}}}

\large{\implies{\sf{x\:=\:\frac{2\times\:\cancel{10}}{\cancel{5}}}}}

\large{\implies{\sf{x\:=\:4\:ms^{-1}}}}

∴ The RMS velocity of the gas at 819°C is 4 m/s

ADDITIONAL INFO :-

✺ Ratio of RMS velocities of different gases at same temperature is given by,

 \large {\underline {\bold {\boxed {\bigstar{  \:  \:  \: \dfrac{r_{1} }{r_{2}} =  \sqrt{ \dfrac{M_{2}}{M_{1}} } }}}}}

✺ RMS velocity of the gas when Pressure, Molecular weight and Volume are given is given by,

 \large {\underline {\bold {\boxed {\bigstar{ \:  \: u_{rms}  =  \sqrt{ \dfrac{3PV}{M} } }}}}}

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