Final answer:
To find the root mean square speed of ammonia molecules at 1.9 °C, one needs to convert the temperature to Kelvin and use the kinetic theory of gases formula with Boltzmann's constant and the molar mass of ammonia.
Step-by-step explanation:
The problem asks us to find the root mean square speed (Urms) of ammonia molecules at a given temperature. To solve this, we need to use the kinetic theory of gases which provides the formula: Urms = √(3kBT/M). In this equation, kB is Boltzmann's constant (1.38 × 10-23 J/K), T is the absolute temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole (kg/mol).
First, convert the temperature from Celsius to Kelvin: T = 1.9 °C + 273.15 = 275.05 K. The molar mass of ammonia (NH3) is 17.031 g/mol, which is 0.017031 kg/mol. Now, substitute these values into the formula for Urms.
Urms = √(3 × 1.38 × 10-23 J/K × 275.05 K / 0.017031 kg/mol)
Calculating this results in the rms speed of ammonia molecules at 1.9 °C.