Helppppp!!! Im so bad at Chem!

Question

A Watt (W) is a unit of power equal to 1J/s. A kilowatt is 1000 watts. How many kilowatt hours (1000 watts/s for one hour) of energy would be produced by the complete conversion to energy of 0.753 mg of matter?

**PLease explain step by step so I can understand better!

Answer 1

0.753 mg at complete conversion yields 6.7676e+10 joules. Converted in one second, this would be 6.7676e+10 watts or  6.7676e+7 kW/s or   6.7676e+7/3600 = 1.886e+4 = 18,860 kW.hr

Answer 2

E = mc^2

m = 0.753 mg x (1 g / 1000 mg) x (1 kg / 1000 g) = 7.53 x 10^-7 kg

E = mc^2 = 7.53 x 10^-7 kg x (3 x 10^8 m/s)^2

E = 6.78 x 10^10 J

Next: 1 joule = 2.78 × 10^-7 kilowatt hours

E = 6.78 x 10^10 J x (2.78 × 10^-7 / 1 J)

E = 1.88 x 10^4 kw hr

Answer 3

Wow.  You may or may not be bad at chem, but this isn't really chem.

"Complete conversion to energy" means Einstein's mass-energy equivalence equation:  e=mc2

so mass is 0.000753 g, and c is 3 E 10 cm/sec, c2 therefore 9E20 cm2/sec2.

Multiply that out, and you get:  6.7 E17 g*cm2/sec2.

g*cm2/sec2 is the unit of energy called an erg.  But the question asks for KWHr.  It's an exercise in energy conversion and the result is that one erg is only 2.77 E-14 KWHr, so you get the final result that the mass conversion gives  18,611 Kilowatt Hours.  Or 18.6 Megawatts for an hour.   A nice little power plant.  That amount of mass, if water, is a little bitty drop that you could see, but if it were any smaller you probably couldn't.