In fireworks (See Reactions 1-3 below), the heat released during a combustion re
ID: 1065575 • Letter: I
Question
In fireworks (See Reactions 1-3 below), the heat released during a combustion reaction (reaction 1) excites metal electrons in some salts (reaction 2). The photon of emitted electromagnetic radiation when an excited electron returns to a lower energy level is in the visible range (reaction 3). Strontium chloride emits a strong light at wavelength 641 nm and barium chloride salts have a strong emission around 493 nm. Assume a. all the light energy emitted comes from complete conversion of the heat energy absorbed, b. only one photon per atom is released, and c. the electron makes only one transition to emit the photon. KClO_4(s) + 3C_(graphite) + O_2(g) rightarrow KCl(s) + 3CO_2(g) + Heat Heat + BaCl_2 + SrCl_2 rightarrow Ba*Cl_2 + Sr*Cl_2 (*=excited states) Ba*Cl_2 + Sr*Cl_2 rightarrow BaCl_2 + SrCl_2 + light Energy calculations Calculate the E absorbed by each metal ion using the photon wavelengths above. Then calculate the E released per mol of each salt when returning to ground state (leaving it in kJ/mol).Explanation / Answer
The energy emitted by the metal ion is given by the equation
E = hc/ where h = 6.626*10-34 J.s , c is the velocity of light in vacuum = 3*108 m/s and = wavelength of the photon.
For Ba*Cl2, = 493 nm = (493*10-9 m). Plug in the value to obtain the energy emitted as
E = (6.626*10-34 J.s).(3*108 m/s)/(493*10-9 m) = 4.032*10-19 J (ans).
The above is the energy emitted per atom of Ba*. 1 mole of Ba*Cl2 contains 6.023*1023 atoms of Ba* per mole. Therefore, energy released per mole of Ba*Cl2 is
(4.032*10-19 J/atom)*(6.023*1023 atoms/mol) = 242847.36 J/mol = (242847.36 J/mol)*(1 kJ/1000 J) = 242.847 kJ/mol 242.85 kJ/mol (ans).
For Sr*Cl2, = 641 nm = (641*10-9) m. Plug in the value to obtain the energy emitted per atom as
E = (6.626*10-34 J.s).(3*108 m/s)/(641*10-9 m) = 3.10*10-19 J/atom (ans)
Energy emitted per moles is
(3.10*10-19 J/atom)*(6.023*1023 atoms/mole) = 186713 J/mol = 186.713 kJ/mol 186.71 kJ/mol (ans).