Question

At what temperature will the root mean - square speed of oxygen molecules have the value of 640m/s? 1 kilomole of oxygen has a mass of 32kg
a) 252.5^oc
b) 332.3 ^0c
c) 272.2 ^0c
d) 373.2 ^0c

Answer 1

Answer on Question #48430-Physics-Molecular Physics-Thermodynamics

At what temperature will the root mean - square speed of oxygen molecules have the value of $640\mathrm{m / s}$ ? 1 kilomole of oxygen has a mass of $32\mathrm{kg}$

a) $252.5^{\wedge}oc$

b) $332.3^{\wedge}0c$

c) $272.2^{\wedge}0c$

d) $373.2^{\wedge}0c$

Solution

The root mean - square speed of molecule is

$$v _ {r m s} = \sqrt {\frac {3 R T}{M}}.$$

The temperature of oxygen is

$$T = \frac {M v _ {r m s} ^ {2}}{3 R} = \frac {3 2 \frac {K g}{K m o l} \left(\frac {6 4 0 m}{s}\right) ^ {2}}{3 \cdot 8 3 1 4 J K m o l ^ {- 1} K ^ {- 1}} = 5 2 5. 5 K = (5 2 5. 5 - 2 7 3. 0) {}^ {\circ} \mathrm {C} = 2 5 2. 5 {}^ {\circ} \mathrm {C}.$$

Answer: a) $252.5{}^{\circ}C$