calculate the average kinetic energies of CH4 and N2 molecules at 273k and 546k
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 calculate the average kinetic energy of CH4 and N2 molecules at different temperatures, we can use the equation for kinetic energy:
KE = (3/2) * k * T
where KE is the kinetic energy, k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the temperature in Kelvin.
Let's first find the average kinetic energy of CH4 molecules at 273 K:
KE_CH4 = (3/2) * k * T_CH4
Substituting the values:
T_CH4 = 273 K
k = 1.38 x 10^-23 J/K
KE_CH4 = (3/2) * (1.38 x 10^-23 J/K) * (273 K)
KE_CH4 ≈ 6.03 x 10^-21 J
Now, let's find the average kinetic energy of N2 molecules at 273 K:
KE_N2 = (3/2) * k * T_N2
Substituting the values:
T_N2 = 273 K
k = 1.38 x 10^-23 J/K
KE_N2 = (3/2) * (1.38 x 10^-23 J/K) * (273 K)
KE_N2 ≈ 6.03 x 10^-21 J
The average kinetic energies of CH4 and N2 molecules at 273 K are approximately 6.03 x 10^-21 J.
Now, let's calculate the average kinetic energies of CH4 and N2 molecules at 546 K using the same formula:
KE_CH4 = (3/2) * k * T_CH4
Substituting the values:
T_CH4 = 546 K
k = 1.38 x 10^-23 J/K
KE_CH4 = (3/2) * (1.38 x 10^-23 J/K) * (546 K)
KE_CH4 ≈ 9.05 x 10^-21 J
Next, let's find the average kinetic energy of N2 molecules at 546 K:
KE_N2 = (3/2) * k * T_N2
Substituting the values:
T_N2 = 546 K
k = 1.38 x 10^-23 J/K
KE_N2 = (3/2) * (1.38 x 10^-23 J/K) * (546 K)
KE_N2 ≈ 9.05 x 10^-21 J
The average kinetic energies of CH4 and N2 molecules at 546 K are approximately 9.05 x 10^-21 J.
Therefore, the average kinetic energies of CH4 and N2 molecules at 273 K are the same (6.03 x 10^-21 J), while at 546 K, they are also the same (9.05 x 10^-21 J).