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.)
1 answer:
Answer:
![v_{rms}=866.32m/s](https://tex.z-dn.net/?f=v_%7Brms%7D%3D866.32m%2Fs)
Explanation:
Hello,
In this case, since the rms speed of the molecules is computed by:
![v_{rms}=\sqrt{\frac{3RT}{M} }](https://tex.z-dn.net/?f=v_%7Brms%7D%3D%5Csqrt%7B%5Cfrac%7B3RT%7D%7BM%7D%20%7D)
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](https://tex.z-dn.net/?f=U%3DnCvT%5C%5C%5C%5CT%3D%5Cfrac%7BU%7D%7BnCv%7D%3D%5Cfrac%7B15kJ%2A%5Cfrac%7B1000J%7D%7B1kJ%7D%20%7D%7B10mol%2A%5Cfrac%7B4.00g%7D%7B1mol%7D%20%2A3.1156%5Cfrac%7BJ%7D%7Bg%2AK%7D%20%7D%20%20%5C%5C%5C%5CT%3D120.36K)
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](https://tex.z-dn.net/?f=v_%7Brms%7D%3D%5Csqrt%7B%5Cfrac%7B3%2A8.314%5Cfrac%7Bkg%2Am%5E2%7D%7Bs%5E2%2Amol%2AK%7D%2A120.36K%7D%7B4.00%5Cfrac%7Bg%7D%7Bmol%7D%2A%5Cfrac%7B1kg%7D%7B1000%7D%20%7D%20%7D%20%5C%5C%5C%5Cv_%7Brms%7D%3D866.32m%2Fs)
Regards.
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