1) How does electrical potential energy gained by a charging capacitor compare to the work done by the battery in the same circuit?
(it says less is gained, not sure why?)
2) If compound X (MW = 331g/mol, specific gravity = 4.53, solubility in water @ 0c = 37.7g/100ml), what is the molality of a saturated solution of compound X at 0 deg?
2b) What is the mole fraction of X in a 10% (wt-wt) aqueous solution?
3)Two cars, each of mass 1000kg travel in opposite directions @ 20m/s. if they are involved in an inelastic collision, how much heat and deformation energy is produced?
Thanks much.
1) This is probably because some energy is lost in a resistor that is also in the circuit. If this is the case, some energy is dissipated in the resistor and lost as heat. This means that only a portion of the energy becomes stored in the capacitor.
2) The solution is made in water, so molality is the number of moles of solute per kilogram of solvent (1000 mL of water = 1 kg)
(37.7 g / 100 mL) / (331 g/mol) = 0.114 mol / 100 mL = 1.14 mol / 1000 mL = 1.14 mol / 1 kg
so the molality is 1.14 m.
2b) Molar mass of water = 18 g/mol
10 % = 0.1 = (331 g/mol)*(number of moles of X) / [ (18 g/mol) * (number of moles of water) + (331 g/mol)*(number of moles of X) ]
Okay, at this point, I would simplify the equation by saying that the number of moles of X is going to be much much less than the number of moles of water. This is because it is only a 10% solution and the molar mass of X is almost 20 times that of water. So I would make the denominator simply (18 g/mol) * (number of moles of water). This leaves:
so 0.1 = 18.4 (number of moles of X) / (number of moles of water)
so the mole fraction is:
(number of moles of X) / (number of moles of water) = 0.1/18.4 = 0.0054.
If you were to keep the whole expression, you would obtain a result of 0.0060, so the idea to simplify was reasonable.
3) Alright, so if they have the exact same momentum, but in opposite directions, when they collide inelastically, they will stick together and have zero total momentum. This means that whatever kinetic energy existed before the collision has been transformed into heat and deformation energy. The kinetic energy of one car was 1/2 m v^2 = 1/2 (1000 kg) (20 m/s)^2 = 2e5 J. So the total kinetic energy (both cars) was 4e5 J. This is the amount of energy that must have been lost.
