What is the ratio of the average velocity of
hydrogen molecules to that of neon atoms at
the same temperature and pressure?
avg velocity = sqrt(T/molar mass)
You can do this one of two ways.
1. Calculate the avg velocity of each gas, then take the ratio.
2. Set up avg vel H2 and set it equal to avg vel Ne, then solve for the ratio you want.
To determine the ratio of the average velocity of hydrogen molecules to that of neon atoms at the same temperature and pressure, we can use the equation for the average velocity of a gas particle:
v = sqrt((2 * k * T) / m)
Where:
- v is the average velocity of the gas particle.
- k is the Boltzmann constant (1.38 x 10^-23 J/K).
- T is the temperature in Kelvin.
- m is the molar mass of the gas particle.
For hydrogen (H2), the molar mass (m) is 2 g/mol.
For neon (Ne), the molar mass (m) is 20 g/mol.
Since the temperature and pressure are the same for both gases, we can cancel out those variables.
Now, let's calculate the ratio of the average velocities:
v_hydrogen = sqrt((2 * k * T) / m_hydrogen)
v_neon = sqrt((2 * k * T) / m_neon)
ratio = v_hydrogen / v_neon
= sqrt((2 * k * T) / m_hydrogen) / sqrt((2 * k * T) / m_neon)
= sqrt((m_neon * (2 * k * T)) / (m_hydrogen * (2 * k * T)))
= sqrt(m_neon / m_hydrogen)
Substituting the known molar masses:
ratio = sqrt(20 g/mol / 2 g/mol)
= sqrt(10)
= 3.16
Therefore, the ratio of the average velocity of hydrogen molecules to that of neon atoms at the same temperature and pressure is approximately 3.16.