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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.