The answer for this question is 46140 cm/s

Gases consist of atoms or molecules that move at different speeds in random directions. The root mean square velocity (RMS velocity) is a way to find a single velocity value for the particles.The average velocity of gas particles is found using the root mean square velocity formula

μrms= (3RT/M)½

whereμrms= root mean square velocity in m/secR= ideal gas constant= 8.3145 (kg·m2/sec2)/K·molT =absolute temperaturein KelvinM = mass of a mole of the gas inkilograms.

Really, the RMS calculation gives youroot mean square speed, not velocity. This is because velocity is a vector quantity, which hasmagnitude and direction. The RMS calculation only gives the magnitude or speed.

The temperature must be converted to Kelvin and the molar mass must be found in kg to complete this problem.

Step 1Find the absolute temperature using the Celsius to Kelvin conversion formula:

T = °C + 273T = 0 + 273T = 273 K

Step 2Find molar mass in kg:

From theperiodic table, molar mass ofoxygen= 16 g/mol.

Oxygen gas(O2) is comprised of two oxygen atoms bonded together. Therefore:

molar massof O2= 2 x 16molar mass of O2= 32 g/mol

Convert this to kg/mol:

molar mass of O2= 32 g/mol x 1 kg/1000 gmolar mass of O2= 3.2 x 10-2kg/mol

Step 3- Find μrms

μrms= (3RT/M)½μrms= [3(8.3145 (kg·m2/sec2)/K·mol)(273 K)/3.2 x 10-2kg/mol]½μrms= (2.128 x 105m2/sec2)½μrms= 461 m/sec

Answer:

The average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 °C is 461 m/sec.