Question

at what temperature is the root mean square velocity of CO2 gas the same as that of Cl2 at 293k​

Answer 1

Answer:

181.5

Explanation:

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Answer 2

Answer: Temperature of CO₂ should be 181.57 Kelvin

Explanation:

Root mean square velocity is the square root of mean of individual gas molecules.

For a given gas, it is a function of the temperature of the gas.

The root mean square velocity of a gas is given by the formula:

$v = \sqrt{\frac{3RT}{M} }$

v ⇒ RMS speed of gas

R ⇒ Universal gas constant

T ⇒ Temperature

M ⇒ Molar mass of gas

For CO₂ gas:

Molar Mass = 44 g

Temperature = T Kelvin

RMS speed of CO₂ at given temperature = $\sqrt{\frac{3RT}{44} }$

For Cl₂ gas :

Molar Mass = 71 g

Temperature of gas = 293 K

RMS speed of Cl₂ at given temperature  = $\sqrt{\frac{3R(293)}{71} }$

ATQ,

RMS speed of CO₂  =  RMS speed of Cl₂

     $\sqrt{\frac{3RT}{44} }$   $= \sqrt{\frac{3R(293)}{71} }$

           $\frac{T}{44} = \frac{293}{71}$

          $T = \frac{293}{71} * 44$

         $T = 181.577$

At 181.577 Kelvin, rms speed of CO₂ gas is equal to rms speed of Cl₂ gas at 293 Kelvin.

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