Question

Given rms speed, c = (3 RT/M)^1/2 Determine the temperature and pressure of 3.01 times 10^23 gas molecules, each with a mass of 6.64 times 10^-26 kg, in a 5 times 10^-3 m^3 container if the rms speed is 560 m/s. These molecules are distributed in 2 states with energies of 0 and 5 epsilon (epsilon =1.381 times 10^-21 J). There is no degeneracy for the first level. The second level is doubly degenerated. Calculate number of molecules in each state at the temperature you determined. A boy had a dream of riding a helium balloon to fly around the world. Assuming the boy had a weight of 50 kg, what is the minimum diameter of the balloon to lift the boy at room temperature (25 degree C) and atmospheric pressure. Ammonia oxidation is a key step in the production of nitric acid, an important commodity chemical. Industrially, the reaction occurs at 750 - 900 degree C in the presence of a Pt catalyst. Determine the Delta_tau H for 4NH_3 (g) + 3O_2(g) rightarrow 4NO(g) + 6 H_2O (g) at 1 bar and 800 degree C, provided with the following data: Standard enthalpy of formation for NH_3, NO and H_2O are -45.9, 90.25 and -241.82 kJ mol^-1; the heat capacities of NH_3, O_2, NO, NO and H_2O are 35.06, 29.36, 29.8 and 33.6 J K0-1 mol0-1, respectively, and arc constant.

Answer 1

a)

Find T and P in which 3.011*10^23 molecules mass of 6.64*10^-26 kg in a V = 5*10^-3 m3 container and V = 560 m/s

First, let us find T from the equation

RMS = sqrt(3RT/MW)

560 m/s = sqrt(3*8.314 J/molK * T / (MW))

find MW

MW = mass / mol = number of molecules * mass of molecules / mol of molecules

MW = ( 6.64*10^-26)(3.011*10^23) kg /

MW = 0.0199 kg / (0.4349 mol) = 0.045757 kg/mol

560 m/s = sqrt(3*8.314 J/molK * T / (0.045757))

Solve for T

T = (560^2)/(3*8.314)*0.045757 = 575.310 K

T = 575.310-273 = 302.31 °C

For Pressure

apply ideal gas law

PV = nRT

P = nRT/V

n = 0.4349 mol, R = 8.314 J/molK

V = 5*10^-3 m3

P = (0.4349 mol )(8.314 J/molK)(575.310 K)/(5*10^-3 m3) = 416036.41 Pa

1 atm = 101325 Pa

so

P= 4.10 atm

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