Respuesta :
Answer:
The correct answer is option e.
Explanation:
The formula used for root mean square speed is:
[tex]\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
[tex]\nu_{rms}[/tex] = root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature
M = Molar mass
[tex]N_A[/tex] = Avogadro’s number = [tex]6.02\times 10^{23}mol^{-1}[/tex]
Root mean square speed of carbon dioxide molecule:
[tex]\nu_{rms}= 550 m/s[/tex]
Temperature of the mixture = T =?
Molar mass of carbon dioxide = 44 g/mol = 0.044 kg/mol
[tex]\nu_{rms}=550 m/s=\sqrt{\frac{3\times 1.38\times 10^{-23}J/K\times 6.022\times 10^{23}mol^{-1}T}{0.044 kg/mol}}[/tex]
T = 533.87 K
Root mean square speed of nitrogen molecule:
[tex]\nu'_{rms}= ?s[/tex]
Molar mass of nitrogen = 28 g/mol = 0.028 kg/mol
[tex]\nu'_{rms}=\sqrt{\frac{3\times 1.38\times 10^{-23}J/K\times 6.022\times 10^{23}mol^{-1}\times 533.87 K}{0.028 kg/mol}}[/tex]
[tex]\nu'_{rms}=689.46 m/s\approx 689 m/s[/tex]
689 m/s is the root-mean-square speed of the nitrogen molecules in the sample.
