A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He)and 1.10 mole of diatomic oxygen (O₂),at a temperature of 260 K.The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol,respectively.What is the ratio of the root-mean-square (thermal)speed of helium to that of oxygen? A) 1.4 B) 2.0 C) 2.8 D) 4.0 E) 5.6

Question

Quizplus · Accepted Answer

The root-mean-square speed of a gas particle is given by the formula,
v_rms = sqrt((3kT)/(m))
where k is the Boltzmann constant, T is the temperature, and m is the mass of the particle.
The ratio of v_rms of helium to oxygen can be written as,
(v_rms)_He / (v_rms)_O2 = sqrt(m_O2/m_He)

Substituting the values, we get
(v_rms)_He / (v_rms)_O2 = sqrt(16.0/4.0) = sqrt(4) = 2.8

Therefore, the answer is (C) 2.8.

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