4. The equation of state for a van der Waal's gas is: RT Vm-b p= a V² m 2 where Vm is the molar volume, V/n. Starting with an expression for U(S,Vm), derive an expression for the internal pressure, îò, and calculate its change when a van der Waal's gas with a = 4.14 atm L²mol-² and b = 5.15 x 10-2 Lmol-¹ is cooled from 200°C to 10°C.

4. The equation of state for a van der Waal's gas is: RT Vm-b p= a V² m 2 where Vm is the molar volume, V/n. Starting with an expression for U(S,Vm), derive an expression for the internal pressure, îò, and calculate its change when a van der Waal's gas with a = 4.14 atm L²mol-² and b = 5.15 x 10-2 Lmol-¹ is cooled from 200°C to 10°C.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Similar questions

A sample of 4.5 moles of an unknown gas occupies a volume of 1.6L at 23.2atm, what is the ideal temperature in oC for this sample of gas? A student attempted to solve the above problem in the pic below, but made an error in the process. Identify the error or errors, solve the problem correctly, and provide the correct answer.
True or false. Why?
Hot gaes Expanding A mixture hot gases expands, changing volume from 2.45 L to 6.82 L, against a constant pressure of 3.22 atm. The P-Vwork involved is Latm .
The van der Waals coefficents of mnatomic argon gas are a=0.1345m6 Pa/mol2 and b=32.19 x 106 m/mol . What is the change in temprature ΔT when one mole of argon gas undergoes a Joule free expansion from 0.1 L to 10L ? a. ΔT = -107k b. ΔT = 107k c. ΔT =54k d. ΔT = -54k
One type of gas mixture used in anesthesiologyis a 50%/50% mixture (by volume) of nitrous oxide (N2O) and oxygen(O2), which can be premixed and kept in a cylinder for later use.Because these two gases don’t react chemically at or below 2000 psi, attypical room temperatures they form a homogeneous single gas phase,which can be considered an ideal gas. If the temperature drops below-6C, however, N2O may begin to condense out of the gas phase. Thenany gas removed from the cylinder will initially be nearly pure O2; asthe cylinder empties, the proportion of O2 will decrease until the gascoming from the cylinder is nearly pure N2O. In another test, the valve of a 500 L cylinder full of the gas mixture at 2000 psi (gauge pressure) is opened wide so that the gas rushes out of the cylinder very rapidly. Why might some N2O condense during this process? (a) This is an isochoric process in which the pressure decreases, so the temperature also decreases. (b) Because of the rapid expansion, heat is…
A 0.210 g sample of a metal, M, reacts completely with sulfuric acid according to the reaction M(s)+H2SO4(aq)⟶MSO4(aq)+H2(g) A volume of 219 mL of hydrogen gas is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 1.0079 bar and the temperature is 25 °C. The vapor pressure of water at 25 °C is 0.03167 bar. Calculate the molar mass of the metal.
Determine the partial molar volume of a component of a gas mixture based on the provided equation of state. When PV (1 – bP) = n2RT, the constant b is taken into consideration.
A canister of pressurized gas has a mass of 10.0000 g. A small amount of gas is released and collected. The collected gas has a volume of 50.00 mL. The pressure and the temperature of the collected gas are the same as the air pressure and air temperature that day: 100. kPa and 25oC. It is noticed that when the gas is released the mass of the pressurized canister decreases to a mass of 9.9110 g. It is not known what gas is in the canister, but you know it is one of the following gases: methane (CH4), ethane (C2H6), propane (C3H8) or butane (C4H10). Using the information provided determine which gas is actually present in the canister.
1 k-mol of methane (CH.) is combusted with theoretical air. The products of combustion are at a pressure of 100 kPa. The balanced reaction is given below. CH, + 2[O; + 3.76N:] → CO2 +2H¿0 + 7.52N2 If the products are at T= 40°C, how many k-mols of water are in the liquid phase? (Assume 40°C < Tao) Answer: 1.321 kmol
b) Connecting a physical protocol to quantitative expressions: In medical treatments, you often never work with pure oxygen. [In fact, breathing high concentrations of oxygen is toxic and can lead to hyperoxia]. Suppose you would like to prepare a mixture of nitrogen and oxygen gases. You have a 1.0-L flask of N₂(g) stored at 2.1 bar and T = 50.°C and a 2.0-L flask of O₂ (g) stored at 1.0 bar and T = 20.°C. Assuming ideal gas behavior, what is the final pressure (in bars) if you combine the two flasks into a 5.0-L flask at room temperature?
Two flasks of equal volume are connected by a narrow tube (of negligible volume). Initially, both flasks are at 27°C and contain 0.70 moles of hydrogen gas, the pressure being 50,000 Pa. One of the flasks is then immersed in a hot oil bath at 127°C, while the other is kept at 27°C. Calculate the final pressure of the system, in Pa. Calculate the final number of moles of hydrogen gas in the flask that was immersed in the oil bath. R = 0.08205 L atm mol-¹ K-₁ T(K) = T (°C) + 273.15