Question

What is $ {V_{rms}} $ of ${\text{S}}{{\text{O}}_2}$ at 300 K?

Answer 1

Hint: The rate of change of an object's direction with respect to a frame of reference is its velocity, which is a function of time. A determination of an object's speed and direction of motion is referred to as velocity.

Complete answer:
The square root of the mean square (RMS or rms or rms) is known as the root mean square (RMS or rms or rms) in mathematics and its applications (the arithmetic mean of the squares of a set of numbers). The quadratic mean, also known as the RMS, is a special case of the generalised mean with exponent 2. RMS can also be expressed as an integral of the squares of the instantaneous values over a loop for a continuously variable function.
The square root of the sum of the squares of the stacking velocity values separated by the number of values yields the root-mean square (RMS) velocity. The RMS velocity is the speed of a wave as it travels through subsurface layers at various intervals along a given ray line. The reason we use the rms velocity rather than the average is that the net velocity of a normal gas sample is zero since the particles are travelling in both directions. This is an important formula since particle velocity defines both diffusion and effusion speeds.
The square root of the mean of squares of the velocity of individual gas molecules is the root mean square velocity (RMS value).
 $ {{\mathbf{V}}_r}_{{\text{ms}}} = \sqrt {\dfrac{{3{\text{RT}}}}{{\text{M}}}} $
 $ {{\mathbf{V}}_r}_{{\text{ms}}} $ = Root-mean-square velocity
T = Temperature in Kelvin.
R= Molar gas constant
M = Molar mass of the gas (Kg/mole)
Substituting the given values
 $ \begin{array}{*{20}{l}}
  {{\text{M}} = 64\;{\text{g}} = 64 \times {{10}^{ - 3}}\;{\text{kg}}} \\
  { = \sqrt {\dfrac{{3 \times 8.31 \times 300}}{{64 \times {{10}^{ - 3}}}}} } \\
  { = \sqrt {11.68 \times {{10}^4}} } \\
  { = 3.41 \times {{10}^2}\;{\text{m}}/{\text{s}}} \\
  { = 341\;{\text{m}}/{\text{s}}}
\end{array} $ .

Note:
Measuring the velocities of particles at a given moment yields a wide range of values; certain particles may travel slowly, while others move rapidly, and the velocity may equate zero since they are continuously travelling in different directions. (Velocity is a vector quantity that equals a particle's speed and direction.) Average the squares of the velocities and use the square root of that value to determine the average velocity.