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

Answer 1

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