Determine the average speed (unit m/s) of N2 at 445K. Please enter a number with one decimal.


To determine the average speed (\(\overline{v}\)) of nitrogen gas (\(N_2\)) at a given temperature, we can use the following formula derived from the kinetic theory of gases:

\[
\overline{v} = \sqrt{\frac{8RT}{\pi M}}
\]

Where:
- \(R\) is the universal gas constant (\(8.314\) J/mol·K),
- \(T\) is the temperature in Kelvin (\(445\) K),
- \(M\) is the molar mass of \(N_2\) (which is \(28.02 \, \text{g/mol} = 0.02802 \, \text{kg/mol}\)).

Let's calculate:

\[
\overline{v} = \sqrt{\frac{8 \times 8.314 \times 445}{\pi \times 0.02802}}
\]

Now, I'll compute the value.The average speed of \(N_2\) molecules at 445 K is approximately \(579.9\) m/s.

Would you like more details or have any questions about the calculation?

Here are 5 related questions you might find interesting:
1. How does the average speed of \(N_2\) change if the temperature increases to 500 K?
2. What would be the average speed of oxygen gas (\(O_2\)) at 445 K?
3. How does the molar mass of a gas affect its average speed at a given temperature?
4. What is the root mean square speed of \(N_2\) at 445 K?
5. How would you determine the average kinetic energy of an \(N_2\) molecule at 445 K?

**Tip:** Remember that lighter gas molecules move faster at the same temperature compared to heavier ones.

Determine the average speed (unit m/s) of N2 at 445K. Please enter a number with one decimal.

Learn how to calculate the average speed of nitrogen gas (N2) at 445K using the kinetic theory of gases. This tutorial includes the formula for average speed and detailed calculations, perfect for students in Grades 11-12 studying thermodynamics and gas laws.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation