Final answer:
The question involves calculating the root mean square velocity of neon gas at a specific temperature using the ideal gas law and the kinetic theory of gases.
Step-by-step explanation:
The subject of this question is to calculate the root mean square velocity (Urms) of neon gas (Ne) at a given temperature, assuming ideal gas behavior. The root mean square velocity is a statistical measure of the speed of particles in a gas, which is derived from the kinetic theory of gases. To calculate this, the equation Urms = √(3kBT/M) is used, where kB is the Boltzmann constant (1.38 × 10-23 J/K), T is the temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole (kg/mol).
First, we convert the given temperature from Celsius to Kelvin: T = -23.0 °C + 273.15 = 250.15 K. The molar mass of Ne is given as 20.2 g/mol, which needs to be converted to kg/mol, so M = 20.2 × 10-3 kg/mol. Now we substitute these values into the equation:
Urms = √(3 × (1.38 × 10-23 J/K) × 250.15 K) / (20.2 × 10-3 kg/mol)
The calculated result for Urms will be the root mean square velocity of Ne gas at -23.0 °C in m/s.