(a)
Interpretation:
The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.
Concept introduction:
From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,
Probability = e –(ΔE/RT)
(b)
Interpretation:
The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.
Concept introduction:
From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,
Probability = e –(ΔE/RT)
(c)
Interpretation:
The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.
Concept introduction:
From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,
Probability = e –(ΔE/RT)
Trending nowThis is a popular solution!
Chapter 1 Solutions
Physical Chemistry
- Which of the following quantities can be taken to be independent of temperature? independent of pressure? (a) H for a reaction (b) S for a reaction (c) G for a reaction (d) S for a substancearrow_forward6.24 Consider this reaction: 2CH,OH(I) + 302(g) 4H,0(1) + 2CO2(8) AH = -1452.8 kJ/mol |3Darrow_forwardA dilute gas at a pressure of 2.0 atm and a volume of 4.0 L is taken through the following quasi-static steps: (a) an isobaric expansion to a volume of 10.0 L, (b) an isochoric change to a pressure of 0.50 atm, (c) an isobaric compression to a volume of 4.0 L, and (d) an isochoric change to a pressure of 2.0 atm. Show these steps on a pV diagram and determine from your graph the net work done by the gas.arrow_forward
- So, when there is no value given for a substance O2, you are to assume that it is zero?arrow_forwardUnder what conditions will the quantities q and w be negative numbers?arrow_forwardIf a system undergoes a process between fixed (known) states 1 and 2, its pressure change depends on the process. True Falsearrow_forward
- "A 1-L flask is filled with 1.45 g of argon at 25 ∘C. A sample of ethane vapour is added to the same flask until the total pressure is 1.11 bar ."(A) What is the partial pressure of Argon PAr , in the flask?(B) What is the partial pressure of ethane, Pethane , in the flask?arrow_forwardValue of k and its unitsarrow_forward(a) A rigid tank contains 1.60 moles of helium, which can be treated as an ideal gas, at a pressure of 28.0 atm. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to 5.00 atm. How many moles are removed? mol (b) What If? In a separate experiment beginning from the same initial conditions, including a temperature T, of 25.0°C, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from 28.0 atm to 5.00 atm. What is the final temperature (in °C) of the gas? °Carrow_forward
- Indicate whether each statement is true or false. (a) Unlikeenthalpy, where we can only ever know changes in H, wecan know absolute values of S. (b) If you heat a gas suchas CO2, you will increase its degrees of translational, rotationaland vibrational motions. (c) CO2(g) and Ar(g) havenearly the same molar mass. At a given temperature, theywill have the same number of microstates.arrow_forward(a) For a certain system, q = –850 J and the volume changes from 16.37 L to 370. cm3 at a constant external pressure of 1336 torr. (760 torr = 760 mmHg = 1.01325 × 105 Pa = 1 atm) (i) Explain in thermodynamic terminology what is happening in this system.arrow_forwardA high pressure gas canister bursts. When the debris is cleared, frost is found to have formed on the metal. A scientist decides to use the ideal gas law to find out how much the temperature of the gas changed when the cylinder burst. Why is this approach incorrect? A They don't know the number of moles of the gas. (B) The gas was being stored as a compressed liquid. C The expansion was adiabatic. (D) The expansion was isothermal.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage Learning