One mole of an ideal gas occupies a volume of 3.5×10^-2m^3 and exerts a pressure of 3atm on the walls of its container.Find average translatoinal kinetic energy per molecule and the absolute temperature of the gas? K avg=(3/2)kT
To find the average translational kinetic energy per molecule (K_avg) and the absolute temperature (T) of the gas, we can use the ideal gas law and the equation for average kinetic energy.
The ideal gas law is given by: PV = nRT
Where:
P = Pressure of the gas
V = Volume occupied by the gas
n = Number of moles of gas
R = Ideal gas constant
T = Absolute temperature of the gas
In this case, we are given:
P = 3 atm
V = 3.5 × 10^(-2) m³ (since the volume is given in cubic meters, we don't need to convert it)
n = 1 mole
R = 0.0821 L.atm/(mol.K) (this is the value of R in the correct units for this problem)
We can rearrange the ideal gas law to solve for T:
T = PV / (nR)
Substituting the given values, we have:
T = (3 atm) * (3.5 × 10^(-2) m³) / (1 mol * 0.0821 L.atm/(mol.K))
Now, we can calculate the value of T.
To find the average translational kinetic energy per molecule (K_avg), we use the equation:
K_avg = (3/2)kT
Where:
k = Boltzmann's constant (1.38 × 10^(-23) J/K)
Substituting the calculated value of T into the equation, we can find K_avg.
It's important to note that we have used the ideal gas law, the equation of average kinetic energy, and relevant constants to solve these equations.