Final answer:
To find the root mean square speed of krypton gas at 0.14 atm and -13°C, convert the conditions to SI units, use the calculated temperature in Kelvin along with the known molar mass of krypton in the urms formula, and compute to get approximately 164 m/s.
Step-by-step explanation:
To calculate the root mean square (rms) speed of krypton gas atoms at a given temperature and pressure, we use the formula derived from the kinetic molecular theory (KMT) of gases:
urms = √(3kBT/M)
where urms is the root-mean-square speed, 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 = -13°C + 273.15 = 260.15 K
Next, we convert the pressure from atm to Pa:
P = 0.14 atm × (101325 Pa/atm) = 14165.5 Pa
Now, we use the given molar mass of krypton which is 83.798 g/mol or 0.083798 kg/mol for our calculations.
Substitute the known values into the urms equation:
urms = √(3 × 1.38×10-23 J/K × 260.15 K / 0.083798 kg/mol)
After calculation, urms is found to be approximately 164 m/s, rounded to three significant digits.