What is the root mean square speed of argon
gas at 300 K?
1. 4.33 × 102 m/s
2. 1.37 × 101 m/s
3. 3.96 × 102 m/s
4. 4.30 × 101 m/s
5. 5.92 × 102 m/s
To find the root mean square (RMS) speed of argon gas at 300 K, we can use the equation:
RMS speed = √((3 * k * T) / m)
Where:
- k is the Boltzmann constant (1.38 × 10^-23 J/K),
- T is the temperature in Kelvin (300 K),
- m is the molar mass of argon gas (39.95 g/mol).
First, we need to convert the molar mass from grams per mole to kilograms per mole by dividing it by 1000:
m = 39.95 g/mol / 1000 = 0.03995 kg/mol
Next, we substitute the values into the equation:
RMS speed = √((3 * 1.38 × 10^-23 J/K * 300 K) / 0.03995 kg/mol)
Calculating this expression:
RMS speed ≈ √(1247.4 J/kg)
To simplify the answer, we can convert joules per kilogram to meters per second (m/s) using the fact that 1 J/kg = 1 m^2/s^2:
RMS speed ≈ √(1247.4 m^2/s^2)
Finally, we calculate the square root of 1247.4 using a calculator:
RMS speed ≈ 35.30 m/s
Therefore, the RMS speed of argon gas at 300 K is approximately 35.30 m/s.
None of the provided answer options match this value exactly.
Isn't that v(rms) = sqrt (3RT/M)
M is the molar mass in Kg.