Use Table 18.2 Fractions of Molecules in an Ideal Gas with Speeds Less than Vari

Question

Use Table 18.2 Fractions of Molecules in an Ideal Gas with Speeds Less than Various Multiples of v/vrms in the textbook. The molar mass of N2 is 28.0 g/mol.

Part A

For a gas of nitrogen molecules N2, what must the temperature be if 94.7% of all the molecules have speeds less than 1500 m/s?

T = ? K

Part B

For a gas of nitrogen molecules N2, what must the temperature be if 94.7% of all the molecules have speeds less than 1000 m/s?

T = ? K

Part C

For a gas of nitrogen molecules N2, what must the temperature be if 94.7% of all the molecules have speeds less than 500 m/s?

T = ? K

Explanation / Answer

A)
In table 94.7 % or 0.947 corresponds to v/vrms = 1.6
since v = 1500 rms
vrms = 1500/1.6 = 937.5 m/s
Now use:
vrms = sqrt (3*R*T/m)
937.5 = sqrt (3*8.314*T/0.028)
T = 986.6 K

B)
In table 94.7 % or 0.947 corresponds to v/vrms = 1.6
since v = 1000 rms
vrms = 1000/1.6 = 625 m/s
Now use:
vrms = sqrt (3*R*T/m)
625 = sqrt (3*8.314*T/0.028)
T = 438.5 K

C)
In table 94.7 % or 0.947 corresponds to v/vrms = 1.6
since v = 500 rms
vrms = 500/1.6 = 312.5 m/s
Now use:
vrms = sqrt (3*R*T/m)
312.5 = sqrt (3*8.314*T/0.028)
T = 109.6 K

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