Two vessels are labeled A and B. Vessel A contains NH3 gas at 70°C, and vessel B contains Ne gas at the same temperature. If the average kinetic energy of NH3 is 7.1 10-21 J/molecule, calculate the mean-square speed of Ne atoms in m2/s2.

Question

Two vessels are labeled A and B. Vessel A contains NH3 gas at 70°C, and vessel B contains Ne gas at the same temperature. If the average kinetic energy of NH3 is 7.1 10-21 J/molecule, calculate the mean-square speed of Ne atoms in m2/s2.

Answer 1

1/2 mass*v^2=AvgKE

meansqarespeed=2*avgKE/mass

If they are at the same temp, they have the same avgKE.

Answer 2

To calculate the mean-square speed of Ne atoms in m^2/s^2, we can use the following formula:

v^2 = (3 * k * T) / m

Where:
- v^2 represents the mean-square speed
- k is the Boltzmann constant (1.38 * 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kilograms per mole

First, let's convert the given temperature of 70°C to Kelvin:
T = 70 + 273.15 = 343.15 K

Next, we need to determine the molar mass of Ne. The molar mass of any substance can be found on the periodic table. In this case, the molar mass of Ne is about 20.18 g/mol. To convert grams to kilograms, we divide the molar mass by 1000:
m = 20.18 g/mol / 1000 = 0.02018 kg/mol

Now we can plug the values into the formula:
v^2 = (3 * (1.38 * 10^-23 J/K) * (343.15 K)) / 0.02018 kg/mol

Simplifying the equation:
v^2 = 7.09625308 * 10^-19 J/mol

Since we are asked for the mean-square speed in m^2/s^2, we need to convert from J/mol to m^2/s^2. To do this, we need Avogadro's constant, which is 6.022 * 10^23 molecules/mol.

v^2 = (7.09625308 * 10^-19 J/mol) / (6.022 * 10^23 molecules/mol)
v^2 = 1.179 * 10^-42 m^2/s^2

Therefore, the mean-square speed of Ne atoms is approximately 1.179 * 10^-42 m^2/s^2.

Answer 3

To find the mean-square speed of Ne atoms, we can use the equation:

v^2 = (3kB*T)/m

Where:
v = mean-square speed of atoms
kB = Boltzmann constant (1.38 * 10^-23 J/K)
T = temperature in Kelvin (70°C = 70 + 273 = 343 K)
m = mass of an atom (Ne atomic mass = 20.18 g/mol = 20.18 * 10^-3 kg/mol)

First, let's convert the mass of Ne to kg:

m = 20.18 * 10^-3 kg/mol

Now, we can substitute the values in the equation:

v^2 = (3 * 1.38 * 10^-23 J/K * 343 K) / (20.18 * 10^-3 kg/mol)

Simplifying the equation:

v^2 = (3.370 * 10^-20 J) / (20.18 * 10^-3 kg/mol)

v^2 = 1.671 * 10^-18 J/(kg/mol)

Finally, we can convert the units from kg/mol to kg/atom:

v^2 = (1.671 * 10^-18 J/(kg/mol)) * (1 mol / 6.022 * 10^23 atoms/mol)

Simplifying the equation:

v^2 = 2.778 * 10^-42 J/atom

Therefore, the mean-square speed of Ne atoms is approximately 2.778 * 10^-42 m^2/s^2.