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aleksley [76]
3 years ago
5

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
Chemistry
1 answer:
zaharov [31]3 years ago
7 0

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.

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