Hi, I can help with some of these, but without knowing what the experiment is, I can't tell what the context of questions 1 and 3 is. Any calculation based on reaction stoichiometry will use amounts in moles. One gram of propene and one gram of cyclohexene do not contain the same number of moles of alkene since these compounds have different molecular weights.
A carbonyl group is a better withdrawing group because of the inductive effect of the electronegative oxygen, and resonance effects can help here also. The phenyl group can actually go either way with resonance effects, and it has no electronegative atom in it. For example, compare resonance structures of phenol, where the ring "withdraws" electrons from the oxygen (we say the OH group "activates" the ring by donating electron density to it), and acetophenone, where the ring "donates" electron density to the carbonyl group (we say the carbonyl group "deactivates" the ring by withdrawing electron density from it). In organic chemistry this is covered under reactions of benzene and the effect of ring substituents (groups) on the ring. In this context we classify groups as being ring activators or ring deactivators. If you look at a chart in your organic text, you will find that carbonyl containing groups (in which the carbonyl carbon is bonded to the ring) are more deactivating than a phenyl group, which is actually a bit of a ring activating group (this would be a phenyl group attached to the benzene ring, which is the compound biphenyl).
Not sure what's going on with question 3, but if the reactant concentrations (molarities) are supposed to be the same, and the same number of moles of reactants are used in each experiment, then the total volume has to be the same also, since molarity is moles/L.
In general, water, being more polar, better dissolves ionic substances, because it forms strong ion-dipole interactions with positive and negative ions. Water molecules also effectively solvate organic ions such as carbocations, favoring their formation, and thus the reaction rate, in SN1 reactions. Methanol is polar also, but not as polar as water (we can compare the polarities in terms of these solvents' dielectric polarizations, which are 80.4 for water and 33.6 for methanol, the lower value indicating methanol is less polar). Sometimes methanol is used as the solvent in organic reactions instead of water, but this is simply because some organic reactants are not soluble enough in water to make it a practical solvent in these cases.
Acid-base indicators are themselves weak acids or weak bases, capable of existing in protonated and deprotonated form. See here to see phenolphthalein structures, for example. Crystal violet is similar. These compounds are highly conjugated, having many alternating single and double bonds allowing many resonance structures. When they absorb visible light, an electron, usually in a pi bonding molecular orbital (the highest occupied MO, or HOMO), is promoted to a pi antibonding MO (the lowest unoccupied MO, the LUMO). The color (energy) of light absorbed by the molecule corresponds to the energy difference between the HOMO and the LUMO. This difference if affected if an atom in the molecule, such as an oxygen or nitrogen, has a hydrogen bonded to it or not, thus giving a different color. The protonated form exists in acidic solution, while the deprotonated form exists in basic solution. The bonding and therefore the conjugation in the molecule is affected, which in turn has an effect on the energy levels of the HOMO and/or LUMO, which in turn affects the energy difference between the these, which determines the energy or color of light the molecule absorbs.
Hope this helps; I'm assuming you're taking organic chemistry, so that at least most of the terms I've used here are reasonably familiar! If not, feel free to ask me to clarify.
Steve
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