Question

12. In a gas mixture consisting of carbon dioxide (CO2) and nitrogen (N2), the carbon dioxide molecules have a root-mean-square speed of 550 m/s. What is the root-mean-square speed of the nitrogen molecules in the sample? CO2 has a molar mass of 44 grams, and N2 has a molar mass of 28 grams. a) 627 m/s b) 752 m/s c) 564 m/s d) 821 m/s e) 689 m/s

Answer 1

Answer:

The correct answer is option e.

Explanation:

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}$

where,

$\nu_{rms}$ = root mean square speed

k = Boltzmann’s constant = $1.38\times 10^{-23}J/K$

T = temperature

M = Molar mass

$N_A$ = Avogadro’s number = $6.02\times 10^{23}mol^{-1}$

Root mean square speed of  carbon dioxide molecule:

$\nu_{rms}= 550 m/s$

Temperature of the mixture = T =?

Molar mass of carbon dioxide = 44 g/mol = 0.044 kg/mol

$\nu_{rms}=550 m/s=\sqrt{\frac{3\times 1.38\times 10^{-23}J/K\times 6.022\times 10^{23}mol^{-1}T}{0.044 kg/mol}}$

T = 533.87 K

Root mean square speed of nitrogen  molecule:

$\nu'_{rms}= ?s$

Molar mass of nitrogen = 28 g/mol = 0.028 kg/mol

$\nu'_{rms}=\sqrt{\frac{3\times 1.38\times 10^{-23}J/K\times 6.022\times 10^{23}mol^{-1}\times 533.87 K}{0.028 kg/mol}}$

$\nu'_{rms}=689.46 m/s\approx 689 m/s$

689 m/s is the root-mean-square speed of the nitrogen molecules in the sample.