Calculate the root mean square velocity of gaseous xenon atoms at 23 ° C.
To calculate the root mean square velocity of gaseous xenon atoms at 23 °C, we can use the equation:
v = √(3kT/m)
where:
v = root mean square velocity
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature in Kelvin (23 °C = 296 K)
m = mass of xenon atom (131.293 u = 2.18026385 x 10^-25 kg)
Plugging in the values:
v = √(3 * 1.38 x 10^-23 * 296 / 2.18026385 x 10^-25)
v = √(1.63176 x 10^-20 / 2.18026385 x 10^-25)
v = √(7482.435)
v = 86.6 m/s
Therefore, the root mean square velocity of gaseous xenon atoms at 23 °C is approximately 86.6 m/s.