Two moles of molecular hydrogen (H_2) react with 1 mole of molecular oxygen (O_2

Question

Two moles of molecular hydrogen (H_2) react with 1 mole of molecular oxygen (O_2) to produce 2 moles of water (H_2 O) together with an energy release of 2418 kJ/mole of water. Suppose a spherical vessel of radius 0.562 m contains 14.4 moles of H_2 and 7.2 moles of O_2 at 20.0 degree C. (a) What is the initial pressure in the vessel? Your response differs from the correct answer by more than 10%. Double check your calculations. Pa (b) What is the initial internal energy of the gas? J (c) Suppose a spark ignites the mixture and the gases burn completely into water vapor. How much energy is produced? J (d) Find the temperature and pressure of the steam, assuming it's an ideal gas. temperature K pressure Pa (e) Find the mass of steam and then calculate the steam's density. mass kg density kg/m^3 (f) If a small hole were put in the sphere, what would be the initial exhaust velocity of the exhausted steam if spewed out into a vacuum? (Use Bernoulli's equation.) m/s

Explanation / Answer

(a) initial pressure in the vessel =

PV = nRT

P = nRT / V

P = (21.6)*(0.08206)*(293) / 740

P = 0.70 atm = 70927.5 Pa = 0.70 bar

(b) Internal Energy = (5/2) nRT

Internal Energy = (5/2) * 21.6 moles * 8.314 KJ K-1 Kmol-1 * 293K

Internal Energy = 131.54 J

(c) two mole of hydrogen and one mole oxygen produces 2418 KJ/ mol enrgy on combustion.

so 14.4 mol of hydrogen and 7.2 mol of oxygen produces = 2418 * 7.2

= 17409.6 KJ = 17.4 J

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