1. The density of nitrogen at s.t.p (i.e., 273K and 1atm) is 1.25 kg m^-3
(a) find the density of nitrogen at a temperature of 25 degree C and 1atm.
(b) Calculate the root mean square speed of nitrogen molecules at 25 degree C.
2. A vessel of volume 50 cm cube contains hydrogen at a pressure of 1 Pa and at a temperature of 27 ddegree C. Given the mass of one mole of hydrogen molecules is 2g.
(a) calculate the root mean square speed.
(b) find the total internam energy of the gas.
(c) if 0.05 mJ of heat is given to the gas with the volume fixed, find the new temperature , in degree C of the gas.
3. Explain the following fact about ideal gas in molecular terms.
The pressure can be kept constant if the temperature is increased while the volume is increased too.
Kinetic theory
2015-07-03 4:49 am
回答 (2)
2015-07-03 9:05 am
✔ 最佳答案
1(a) 25'C = 298 KHence, density of nitrogen at 25'C and 1 atm
= 1.25 x 273/298 kg/m^2 = 1.145 kg/m^2
(b) Molar mass of nitrogen = 28 g/mole = 0.028 kg/mole
Hnece, rms speed of nitrogen at 25'C
= square-root[ 3 x 8.31 x 298/0.028] m/s = 516 m/s
where 8.31 J/mol.K is the Universal Gas Constant
2. (a) rms speed = square-root[3 x 8.31 x (27+273)/0.002] m/s = 1934 m/s
(b) No. of moles of hydrogen gas = 1 x (50x10^-6)/(8.31 x 300) = 2 x 10^-8
Internal energy of gas
= (5/2).(2x10^-8).(8.31).(300) J = 1.25 x 10^-4 J
(c) Specific heat at constant volume = (5/2).(8.31) J/mol.K = 20.78 J/mol.K
Hence, change in temperature
= 0.05 x 10^-3/(2x10^-8 x 20.78) K = 120 K
New temperature = (27 + 120)'C = 147'C
3. Temperature increase ==> molecules moves faster ==> but molecules need to travel longer distance due to increses of volume ==> the frequency of striking the gas vessel by molecules remains unchanged ==> pressure kept constant.
2015-07-04 00:20:54 補充：
Q:why need to use 273 over 298
A: Since pressure is contant ( 1 atm), density of gas is inversely proportional to its absolute temperature., i.e. (new densirt)/(initial density) = (intital temp)/(new temp)
2015-07-04 00:23:08 補充：
sorry, a typo in the unit in Q1(a). The density unit should be "kg/m^3".
2015-07-04 00:25:33 補充：
Q:i also want to ask whether the / is the part before it is divided by that no. or only the number before the sign'/' is divided by that no. ?
A: Not sure what you ask.
e.g. 1.25 x 273/298 means 1.25 x (273/298)
2015-07-04 4:22 am
why need to use 273 over 298?
2015-07-03 20:29:07 補充：
i also want to ask whether the / is the part before it is divided by that no. or only the number before the sign'/' is divided by that no. ?
2015-07-03 20:29:07 補充：
i also want to ask whether the / is the part before it is divided by that no. or only the number before the sign'/' is divided by that no. ?
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