Question

Определите среднюю квадратичную скорость молекул кислорода и аргона в воздухе при температуре 20 градусов

Answer 1

Ar    V=sqrt(3*R*T/M)=sqrt(3*8,31*293/40*10^-3)=427 м/с
O2  V=sqrt(3*8,31*293/32*10^-3)=477 м/с

Answer 2

Calculating the Average Root-Mean-Square Speed of Oxygen and Argon Molecules at 20 Degrees Celsius

To calculate the average root-mean-square (RMS) speed of oxygen and argon molecules at 20 degrees Celsius, we can use the following formula:

v = sqrt((3 * k * T) / m)

Where: - v = RMS speed - k = Boltzmann constant (1.38 x 10^-23 J/K) - T = temperature in Kelvin - m = mass of the molecule in kilograms

Calculating the RMS Speed of Oxygen Molecules

Using the given temperature of 20 degrees Celsius (293.15 Kelvin) and the molecular mass of oxygen (O2) which is approximately 32 g/mol (0.032 kg/mol), we can calculate the RMS speed of oxygen molecules.

Plugging the values into the formula: v_oxygen = sqrt((3 * 1.38e-23 * 293.15) / 0.032)

Calculating the RMS speed of oxygen molecules gives us: v_oxygen ≈ 482 m/s.

Calculating the RMS Speed of Argon Molecules

For argon (Ar) with a molar mass of approximately 40 g/mol (0.04 kg/mol), we can calculate the RMS speed using the same formula.

Plugging the values into the formula: v_argon = sqrt((3 * 1.38e-23 * 293.15) / 0.04)

Calculating the RMS speed of argon molecules gives us: v_argon ≈ 430 m/s.

Therefore, at a temperature of 20 degrees Celsius, the average root-mean-square speed of oxygen molecules is approximately 482 m/s, while the average root-mean-square speed of argon molecules is approximately 430 m/s.