Question

Вычислите среднюю квадратичную скорость молекулы газа при температуре 27 градусов Цельсия, если этот газ водород

Answer 1

Средняя квадратичная скорость определяется по формуле:
ν=√3*R*T/M 
R=8,31 Дж/моль*К (универсальная газовая постоянная)
M(H2) - 2*10^-3 кг/моль.  (малярная масса водорода)
T - 27+273=300 К - (температура)

ν=√3*8,31*300/2*10^-3
ν≈1933 м/c^2

Answer 2

Calculating the Average Molecular Speed of Hydrogen Gas at 27°C

To calculate the average molecular speed of a gas at a given temperature, we can use the root mean square speed formula:

\[v_{rms} = \sqrt{\frac{3RT}{M}}\]

Where: - \(v_{rms}\) = root mean square speed - \(R\) = gas constant (\(8.314 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1}\)) - \(T\) = temperature in Kelvin - \(M\) = molar mass of the gas

First, we need to convert the given temperature from Celsius to Kelvin: \[T(K) = T(°C) + 273.15\]

Given: - Temperature (\(T\)) = 27°C

Converting to Kelvin: \[T(K) = 27 + 273.15 = 300.15 \, K\]

The molar mass of hydrogen gas (\(H_2\)) is approximately 2.02 g/mol.

Now, we can calculate the average molecular speed of hydrogen gas at 27°C using the root mean square speed formula.

\[v_{rms} = \sqrt{\frac{3 \times 8.314 \times 300.15}{2.02}}\]

Calculating: \[v_{rms} \approx 1935 \, \text{m/s}\]

So, the average molecular speed of hydrogen gas at 27°C is approximately 1935 m/s.