Final answer:
The root mean square speed (Urms) of argon atoms can be calculated using the formula Urms = √(3kBT/M), where T is temperature in Kelvin, and M is the molar mass in kg/mol. Temperature must be converted to Kelvin, and pressure to pascals for accurate calculation.
Step-by-step explanation:
The question asks about the root mean square speed (Urms) of argon atoms at a certain temperature and pressure. To calculate the Urms for a sample of argon gas at 0.15 atm and -37°C, we first need to convert the temperature to Kelvin and the pressure to pascals (the SI unit). The pressure conversion is straightforward: 0.15 atm is equivalent to 0.15 × 101325 Pa. For temperature, we add 273 to the Celsius temperature to get Kelvin. So, the temperature in Kelvin is -37°C + 273 = 236 K.
Next, we use the formula Urms = √(3kBT/M), 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 argon, which is approximately 0.0399 kg/mol for the calculation. Converting this to the molar mass in SI units (kg per mole), we can find the Urms of argon atoms in these conditions.