Chapter 5
Q. 5.10
Calculate the average speed, u, of an N_{2} molecule at 25°C.
| ANALAYSIS | |
| temperature (25°C) | Information given: |
| R = 8.31 × 10³ g · m²/s² · mol · K MM of N_{2} |
Information implied: |
| average speed, u, of N_{2} at 25°C | Asked for: |
STRATEGY
1. Change T to the appropriate units.
2. Note the units of the constant R.
3. Substitute into the equation: u = \left(\frac{3RT}{MM}\right) ^{1/2}
Step-by-Step
Verified Solution
| u = \left(\frac{3 \times 8.31 \times 10^{3} \frac{g·m²}{s² · mol · K} \times 298 K }{28.02\frac{g}{mol} }\right)^{1/2} = 515 m/s | Average speed |
Converting the speed of the nitrogen molecule obtained above to miles per hour:
515\frac{m}{s} × \frac{1 mi}{1.609 × 10³ m} × \frac{3600 s}{1 h} = 1.15 × 10³ mi/h
Note that the average cruising speed of a Boeing 777 is about 580 mi/h and the speed of sound is 768 mi/h.