The balances in a well-equipped chemistry lab usually measure out to + or - 0.1 mg. How many kJ of energy could you make if you converted 0.1 mg of matter entirely to energy?

Question

The balances in a well-equipped chemistry lab usually measure out to + or - 0.1 mg. How many kJ of energy could you make if you converted 0.1 mg of matter entirely to energy?

Answer 1

The mass - energy relationship is given by Einstein’s Equation:

E= mass x (velocity of light)².

but the mass has to be in kg and velocity of light in meter/sec ( they are the base units of SI system of units)

0.1 mg x 0.001 g/ 1 mg x 0.001 kg/ 1 g = 0.0000001 kg = 1.0 x 10^-7 kg

velocity of light = 3.0 x 10⁸ m/sec

E = 1.0 x 10^-7 kg x (3.0 x 10⁸ m/sec)². = 9.0 x 10⁹ J

convert joules to kilojoules:

9.0 x 10^{9 J} x 1 kJ / 1.0³ J = 9.0x10⁶ kJ