A gas containing both hydrogen molecules (each molecule contains two hydrogen atoms) and helium atoms has a temperature of 300 K. How does the average speed of the hydrogen molecules compare to the helium atoms?
The average speed of the hydrogen molecules is the same as that of the helium atoms.
The average speed of the hydrogen molecules is faster than that of the helium atoms, but it is less than two times faster. Since the temperature is the same for both types of atoms, they have the same average kinetic energy, which is given by K=1/2mv2. Helium is twice as massive as hydrogen, so the average speed of the hydrogen atoms is 2√ times higher than that of the helium atoms.
The average speed of the hydrogen molecules is faster than that of the helium atoms, but it is less than two times faster.
To compare the average speeds of the hydrogen molecules and helium atoms, we can use the formula for the average speed of gas particles:
v_avg = sqrt((8 * k * T) / (pi * m))
Where:
- v_avg is the average speed of the gas particles
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature of the gas in Kelvin
- m is the mass of the gas particles
The average speed of gas particles is directly proportional to the square root of their temperature and inversely proportional to the square root of their mass.
Since the hydrogen molecules contain two hydrogen atoms, their mass is twice that of a single hydrogen atom. The mass of a helium atom is approximately four times the mass of a hydrogen atom.
To compare their average speeds, we need to calculate the average speeds of both hydrogen molecules and helium atoms using the given temperature:
For hydrogen molecules:
m_hydrogen_molecule = 2 * m_hydrogen_atom
v_avg_hydrogen_molecule = sqrt((8 * k * T) / (pi * m_hydrogen_molecule))
For helium atoms:
v_avg_helium_atom = sqrt((8 * k * T) / (pi * m_helium_atom))
Since the temperature is the same for both gases, we can compare their average speeds by calculating the ratio:
Ratio = v_avg_hydrogen_molecule / v_avg_helium_atom
Let's plug in the values and calculate the ratio.