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You are watching: Calculate the rms speed of carbon dioxide molecules at stp

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As we recognize from the kinetic concept of gases, the intend kinetic power of gas molecules is proportional to its absolute temperature `T.` Because the kinetic power of a molecule is `(m v^2)/2,` the root suppose square is proportional to `sqrt(T).` The precise formula is

`v_(rms) = sqrt((3RT)/M),`

wbelow `R...

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Hello!

As we understand from the kinetic concept of gases, the mean kinetic energy of gas molecules is proportional to its absolute temperature `T.` Since the kinetic energy of a molecule is `(m v^2)/2,` the root mean square is proportional to `sqrt(T).` The precise formula is

`v_(rms) = sqrt((3RT)/M),`

where `R approx 8.3 J/(mol * K)` is the ideal gas continuous and also `M` is the molar mass of a gas. `M` need to be expressed in `(kg)/(mol).`

We understand the loved one atomic masses of `O` and `C.` They are `16` and `12,` and also we can compute the molar mass of `C O_2:`

`12 + 2*16 = 44 (g/(mol)) = 4.4*10^(-2) ((kg)/(mol)).`

STP generally suggests `0` degrees Celsius, or about `273 K.` Now we deserve to achieve the numerical result:

`v_(rms) = sqrt((3*8.3*273)/(4.4*10^(-2))) approx 393 (m/s).`

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