The density of a gas is 1.25 kg m – 3 at N.T.P. Find the Root mean square velocity of its molecules.
Surely one of the formulae found here (or in your text) can be used to get the answer:
https://en.wikipedia.org/wiki/Root-mean-square_speed
To find the root mean square (RMS) velocity of gas molecules, we can use the following formula:
RMS velocity = √(3kT/m)
Where:
- RMS velocity is the root mean square velocity we need to find.
- k is Boltzmann's constant (1.38 × 10^−23 J/K).
- T is the temperature in Kelvin.
- m is the molar mass of the gas in kilograms.
Since the density of the gas is given in kg/m^3, we can find its molar mass (M) using Avogadro's law, which states that equal volumes of gases under the same conditions of temperature and pressure contain equal numbers of molecules. At N.T.P. (Normal Temperature and Pressure), the volume of 1 mole of any gas is 22.4 liters or 0.0224 m^3.
The molar mass (M) can be calculated using the equation:
Density = (molar mass (M) / 0.0224 ) kg/m^3
Now, let's plug the given density value into the equation to find the molar mass (M).
1.25 kg/m^3 = M / 0.0224 kg/m^3
M = 1.25 kg/m^3 × 0.0224 kg/m^3
M = 0.028 kg/mol
Now that we have the molar mass (M), we can proceed to calculate the RMS velocity using the formula mentioned earlier.
RMS velocity = √(3 × k × T / m)
At N.T.P., the temperature is 273 K.
RMS velocity = √(3 × 1.38 × 10^-23 J/K × 273 K / 0.028 kg/mol)
Now, we have all the values required to calculate the RMS velocity. Plugging in the numbers and solving the equation will give us the answer.