Question

question 8 (1 point)
use kinetic theory, t = ke = ½ m v², to answer the following two questions. two molecules are at the same temperature and thus have the same kinetic energy.

1. if molecule a has a molar mass of 30. g/mol, and molecule b has a molar mass of 50. g/mol, and the molecules have equal intermolecular attractions, which molecule will have the greater velocity? 1
2. if molecules a and b have the same molar mass, will they have the same velocity when at the same temperature? 2

a. a b. b c. yes d. no

Explanation:

Step1: Analyze the relationship between mass and velocity in kinetic energy formula

Given \(KE=\frac{1}{2}mv^{2}\), when \(KE\) is constant (same temperature means same \(KE\)), \(v = \sqrt{\frac{2KE}{m}}\). So, velocity is inversely proportional to the square - root of mass.
Since \(m_A=30\space g/mol\) and \(m_B = 50\space g/mol\), and \(m_Av_B\)

Step2: Consider the case when molar masses are the same

If \(m_A=m_B\) and \(KE_A = KE_B\) (because \(T_A=T_B\)), from \(v=\sqrt{\frac{2KE}{m}}\), when \(m\) and \(KE\) are the same for two molecules, their velocities are the same

Answer:

1. A. A
2. C. yes