I will rate lifesaver to anyone who can help me answer a few short practice ques
ID: 913253 • Letter: I
Question
I will rate lifesaver to anyone who can help me answer a few short practice questions! Thank you!
1. A sample of methane of mass 4.50 g occupies 12.7 L ( 1 L = 1 dm3 ) at 310 K. Calculate the work done when the gas expands (a) isobarically (at constant pressure) against a constant external pressure of 30.0 kPa until its volume has increased by 3.3L, and (b) isothermally by 3.3L. Hint: consider methane as an ideal gas.
2. The kinetic or thermal energy of a molecule in liquid phase can be estimated using the equipartition theorem. (a) Estimate the average velocity of translation of a water molecule along one axis at 37C. (b) Estimate the time it would take for a perfume molecule to travel a distance of 10 m in vacuum at 300 K (Hint: E = ½ mv2 ).
3. What is the ratio of populations that correspond to two vibration energy states in water with energy of 2 kBT and 1 kBT respectively at 300K? Assume that each energy state has only one microstate (or in other words, no degenerate microstates, g = 1).
Explanation / Answer
(a)
To calculate the work done when the gas expands (a) isobarically (at constant pressure) against a constant external pressure of 30.0 kPa until its volume has increased by 3.3L use following expression:
W = -pexdV
Here pex = 30.0 kPa = 30,000 Pa and dV = 3.3 L = 0.0033 m^3
Then;
W = -pexdV
W = - 30,000 Pa *0.0033 m^3
W = - 99 Pa (m^3)
1 pascal (m^3) =1 joule
So
W = - 99 J
(b)
To calculate the work done when the gas expands isothermally by 3.3L use the following expression as follows:
W = -nRT ln Vfinal / V initial
Here n= 4.50 g/ 16.02 g/ mol = 0.281 mol T310 K; R = 8.314 J/K.mol Vfinal = 12.7+3.3 L=16.0 L V initial=12.7 L
W = -0.281* 8.314 * 310 ln 16.0 / 12.7
W = -0.281* 8.314 * 310*ln 1.26
W = -0.281* 8.314 * 310*0.23
W = -167.4 J