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marshall27 [118]
3 years ago
10

The internal energy of 10 moles of helium (a monatomic gas) is 15 kJ. What is the rms speed of the molecules? (The molar mass of

helium is 4.00 g/mole.)
Chemistry
1 answer:
Radda [10]3 years ago
6 0

Answer:

v_{rms}=866.32m/s

Explanation:

Hello,

In this case, since the rms speed of the molecules is computed by:

v_{rms}=\sqrt{\frac{3RT}{M} }

Whereas the absolute temperature is computed from the internal energy (by using the Cp of helium (3.1156 J/g*K) as shown below:

U=nCvT\\\\T=\frac{U}{nCv}=\frac{15kJ*\frac{1000J}{1kJ} }{10mol*\frac{4.00g}{1mol} *3.1156\frac{J}{g*K} }  \\\\T=120.36K

Thereby, the rms speed results:

v_{rms}=\sqrt{\frac{3*8.314\frac{kg*m^2}{s^2*mol*K}*120.36K}{4.00\frac{g}{mol}*\frac{1kg}{1000} } } \\\\v_{rms}=866.32m/s

Regards.

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