The space shuttle carries about 7.35×10 4 kg of solid aluminum fuel, which is ox

Question

The space shuttle carries about 7.35×104 kg of solid aluminum fuel, which is oxidized with ammonium perchlorate according to the following reaction:
10Al(s)+6NH4ClO4(s)4Al2O3(s)+2AlCl3(s)+12H2O(g)+3N2(g)
The space shuttle also carries about 6.02×105 kg of oxygen (which reacts with hydrogen to form gaseous water).

Part A

Assuming that aluminum and oxygen are the limiting reactants, determine the total energy produced by these fuels. (Hffor solid ammonium perchlorate is -295 kJ/mol.)

Part B

Suppose that a future space shuttle was powered by matter-antimatter annihilation. The matter could be normal hydrogen (containing a proton and an electron) and the antimatter could be antihydrogen (containing an antiproton and a positron). What mass of antimatter would be required to produce the energy equivalent of the aluminum and oxygen fuel currently carried on the space shuttle?

Explanation / Answer

Boy your instructor is tough!
10Al(s)+6NH4ClO4 (s)--->4Al2O3(s)+ 2AlCl3 (s) + 12H2O(g)+ 3N2(g)

Hrxn = Hf(products) - Hf(reactants) =

[4Hf(Al2O3)+ 2Hf(AlCl3) + 12Hf(H2O)+ 3Hf(N2)]- [10Hf(Al)+6Hf(NH4ClO4)]

Hf(Al), Hf(N2) = 0 elements in their standard states, Hf(NH4ClO4) given, let's look for the enthalpy of formation:

Hf(Al2O3) = -1669.8 kJ/mol; Hf(AlCl3) = -705.63 kJ/mol; Hf(H2O) = -241.82 kJ/mol;

Hrxn = [(-4*1669.8) + (-2*705.63) + (-12*241.82)] - [(-6*295)]

Hrxn = -9222.3 kJ/mol

Now with this value, let's Convert 7.35×10^4 kg of solid aluminum fuel into mol of Al:

moles Al = 7.35x107 g / 27 g/mol = 2.72x106 moles

Hrxn * moles = Q

Q = 2.72x106 * 9222.3 kJ/mol = -2.51x1010 kJ

1/2O2 + H2 = H2O
Same process Hf(O2) and Hf(H2) = 0 (elements in standard state)

Hrxn = Hf(H2O) = -241.81 kJ/ mol

moles of O2 = 6.02x108 g / 32 g/mol = 1.88x107 moles

Q = 1.88x107 * (-241.81) = -4.55x109 kJ

Part B:

Use Einstein eqn E =1/2mc^2 c = speed of light = 2.998 x 10^8 m/s.

Don't forget 2.00 g of matter annihilated. Check E must be in J but units don't match. Ah here it is: "E (in joules) = m (in kilograms) multiplied by (299,792,458 m/s)2"

From here solve for "m" and you will get the mass required. I'll let you do this part to you now that you have the equation to use.

Hope this helps.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.