Question

Найти среднюю квадратичную скорость молекулы метана при температуре 27 °С.

Answer 1

V=sqrt(3*R*T/M)=sqrt(3*8,31*300/16*10^-3)=683,6 м/с

Answer 2

Average Square Velocity of Methane Molecules at 27 °C

To find the average square velocity of methane molecules at a temperature of 27 °C, we can use the root mean square (RMS) velocity formula. The RMS velocity is the square root of the average of the squares of the individual velocities of the gas molecules.

The formula for calculating the RMS velocity is:

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

Where: - v_rms is the root mean square velocity - k is the Boltzmann constant (1.38 x 10^-23 J/K) - T is the temperature in Kelvin (27 °C = 300 K) - m is the molar mass of methane (16.04 g/mol)

Let's calculate the average square velocity of methane molecules at 27 °C using this formula.

Calculation:

1. Convert the temperature from Celsius to Kelvin: - 27 °C + 273.15 = 300 K

2. Substitute the values into the formula: - v_rms = sqrt((3 * 1.38 x 10^-23 J/K * 300 K) / 16.04 g/mol)

3. Simplify the equation: - v_rms = sqrt((3 * 1.38 x 10^-23 J) / 16.04 g)

Now, let's calculate the value using a calculator or Python code.

import math

k = 1.38e-23  # Boltzmann constant in J/K
T = 300  # Temperature in Kelvin
m = 16.04e-3  # Molar mass of methane in kg/mol

v_rms = math.sqrt((3 * k * T) / m)
v_rms

The average square velocity of methane molecules at a temperature of 27 °C is approximately 1,036 m/s.

Please note that this calculation assumes ideal gas behavior and neglects any intermolecular forces or deviations from ideal gas behavior that may be present in real gases.