Neon exists as a monatomic gas. There are 1.5 mols of neon in a light bulb at a temperature of 75 degrees Celsius.
a. what is the average kinetic energy of the neon atoms?
b. what is the total kinetic energy of all of the atoms?
To answer both questions, we need to use the kinetic theory of gases. The average kinetic energy (KE) of gas particles is directly proportional to temperature. The total kinetic energy can be calculated by multiplying the average kinetic energy by the total number of particles.
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 75°C + 273.15
T(K) = 348.15 K
Now, let's calculate the average kinetic energy (KE_avg) of the neon atoms using the formula:
KE_avg = (3/2) * k * T
where k is the Boltzmann constant (1.380649 x 10^-23 J/K), and T is the temperature in Kelvin.
KE_avg = (3/2) * (1.380649 x 10^-23 J/K) * (348.15 K)
Calculate KE_avg to find the average kinetic energy of the neon atoms.
For part a:
KE_avg = (3/2) * (1.380649 x 10^-23 J/K) * (348.15 K) = 9.669 x 10^-21 J
The average kinetic energy of the neon atoms is approximately 9.669 x 10^-21 Joules.
For part b:
To calculate the total kinetic energy (KE_total) of all the atoms, we need to multiply the average kinetic energy by the total number of atoms (in moles), and then by Avogadro's number (6.0221 x 10^23 particles per mole).
KE_total = KE_avg * n * N_A
where n is the number of moles and N_A is Avogadro's number.
Given that there are 1.5 moles of neon (n = 1.5), we can calculate the total kinetic energy.
KE_total = (9.669 x 10^-21 J) * (1.5 mol) * (6.0221 x 10^23 particles/mol)
Calculate KE_total to find the total kinetic energy of all the atoms.
KE_total = (9.669 x 10^-21 J) * (1.5) * (6.0221 x 10^23)
KE_total ≈ 8.757 x 10^4 Joules
Therefore, the total kinetic energy of all the neon atoms is approximately 8.757 x 10^4 Joules.