Find yhe average molecular speed of a gas at 300K composed of molecules each of mass 5.3×10^-26 kg.
The average molecular speed of a gas can be calculated using the root-mean-square speed formula:
\[ \text{Average Speed} = \sqrt{\frac{3kT}{m}} \]
Where:
- \( k \) is the Boltzmann constant (\( 1.38 \times 10^{-23} \, \text{J/K} \)),
- \( T \) is the temperature in Kelvin (300K in this case),
- \( m \) is the mass of a single molecule (5.3×10^-26 kg in this case).
So, plugging in the values, we get:
\[ \text{Average Speed} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 300}{5.3 \times 10^{-26}}} \]
\[ \text{Average Speed} = \sqrt{\frac{1.242 \times 10^{-20}}{5.3 \times 10^{-26}}} \]
\[ \text{Average Speed} = \sqrt{235.056 \times 10^6} \]
\[ \text{Average Speed} \approx 15.328 \, \text{m/s} \]
Therefore, the average molecular speed of the gas at 300K is approximately 15.328 m/s.