Question
calculate the average kinetic energies of CH4 and N2 molecules at 273k and 546k
Answers
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First, we need to know the mass of the CH4 and N2 molecules. The molar mass of CH4 is 12.01 g/mol (for carbon) + 4 * 1.01 g/mol (for hydrogen) = 16.04 g/mol. The molar mass of N2 is 2 * 14.01 g/mol = 28.02 g/mol.
To find the average kinetic energy, we use the equation:
KE_avg = (3/2) * kT
Where KE_avg is the average kinetic energy, k is Boltzmann's constant (1.38 * 10^-23 J/mol), and T is the absolute temperature in Kelvin.
We will calculate the average kinetic energy for both molecules at both temperatures (273 K and 546 K).
1. For CH4 at 273 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (273 K)
KE_avg ≈ 5.65 * 10^-21 J
2. For CH4 at 546 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (546 K)
KE_avg ≈ 11.3 * 10^-21 J
3. For N2 at 273 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (273 K)
KE_avg ≈ 5.65 * 10^-21 J
4. For N2 at 546 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (546 K)
KE_avg ≈ 11.3 * 10^-21 J
So, the average kinetic energies of CH4 and N2 molecules at 273 K are approximately 5.65 * 10^-21 J, and at 546 K, they are approximately 11.3 * 10^-21 J.
To find the average kinetic energy, we use the equation:
KE_avg = (3/2) * kT
Where KE_avg is the average kinetic energy, k is Boltzmann's constant (1.38 * 10^-23 J/mol), and T is the absolute temperature in Kelvin.
We will calculate the average kinetic energy for both molecules at both temperatures (273 K and 546 K).
1. For CH4 at 273 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (273 K)
KE_avg ≈ 5.65 * 10^-21 J
2. For CH4 at 546 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (546 K)
KE_avg ≈ 11.3 * 10^-21 J
3. For N2 at 273 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (273 K)
KE_avg ≈ 5.65 * 10^-21 J
4. For N2 at 546 K:
KE_avg = (3/2) * (1.38 * 10^-23 J/K) * (546 K)
KE_avg ≈ 11.3 * 10^-21 J
So, the average kinetic energies of CH4 and N2 molecules at 273 K are approximately 5.65 * 10^-21 J, and at 546 K, they are approximately 11.3 * 10^-21 J.