Given rms speed, c = (3RT/M)1/2 (1.15) Determine the temperature and pressure of

Question

Given rms speed, c = (3RT/M)1/2 (1.15) Determine the temperature and pressure of.3.011 times 10^23 gas molecules, each with a mass of4.65 times 10^26 kg, in a 2 times 10^-3 m^3 container if the rms speed is 1000 m/s (b) 10,000 molecules distributed in 3 states with energies of 0, 3 epsilon, 5 epsilon (epsilon = 1.38 times 10^-21 J). There is no degeneracy for the first level. The second and third levels are both triply degenerated. Calculate number of molecules in each state at 500 K. A good estimate to use when comparing tire pressure to temperature is for every 10 degree F, tire pressure will adjust by 1 psi, i.e. if the temperature is for every 10 degree F, the tire pressure will increase by 1 psi. (1 psi = 0.06895 bar, 1 K = 1.8 degree F). The Formula One performs the best at a tire temperature of ~110 degree C. For a tire of the Formula One car was inflated to 2.2 bar (~32 psi) initially at 35 degree C, (a) estimate the pressure at the optimal operating temperature of 110 degree C; (b) In actual operation, the tire has an undetectable leak, making the tire pressure only reach 2.5 bar. How much air in kg was leaked out? Assuming ideal gas behavior for the products and reactants, determine the delta_rH(500 degree C) for N_2(g) + 3H_2(g) rightarrow 2NH_3 (g) at 1 bar. The standard enthalpy of formation for ammonia is -45.9 kJ mol^-1, the C_p, m of H_2, N_2 and NH_3 are 28.8, 29.1, 35.1 J K^-1 mol^-1, respectively. (a) What is the final temperature when mixing 100 g steam at 100 degree C and 680 g of ice at 0 degree C in an insulated vessel? (b) Calculate the total change in entropy. Given that C_p, m = 75.0 J K^-1 mol^-1 for liquid water and delta_fus H = 6.0 kJ mol^-1 at the normal melting point and delta_vap H = 40.8 kJ mol^-1 taking molecular weight of water M_water =18.0 g mol^-1. Consider 2.0 moles of a monatomic perfect gas initially at T^1 = 300 K and p_1 = 5.0 bar. The heat capacities at constant volume and constant pressure for this gas are C_v=3/2 R and C_P = 5/2 respectively. The system follows a reversible isothermal compression step to double the pressure of the container, determine the value of p_2, V_2, w, q, delta U, delta H, delta S, delta G for this step. Make sure to show your work and provide units. Step (a) is following by a constant pressure step to expand to its original volume, determine the value of T_2, w, q, delta U, delta H, delta S for this step. The loop is closed by following a reversible constant volume step. Determine the value of w, q, delta U, delta H, delta S, for step. Make sure to show your work and provide units.

Explanation / Answer

III) N2 (g) + 3H2 (g) -------------> 2NH3 (g)

Hfo [N2 (g)] = 0

Hfo[H2 (g)]= 0

Hfo[NH3 (g)]= -45.9 kJ/mol

Hrxn = Hfo(products) - Hfo( reactants)

= 2 Hfo [NH3 (g)] - { Hfo [N2 (g)] + Hfo[H2 (g)] }

= 2 x -45.9 kJ/mol - { 0 + 0 }

= - 91.8 kJ/mol

Hence,

Hrxn = - 91.8 kJ/mol

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