How are alkyl groups electron donating?

Recall that an isolated alkyl group has a carbon atom at one end / point that has not completed its valence shell (this disobeys the octet rule, with carbon being one of the few elements that reliably obeys it). This means that there are electrons in its valence shell that have not participated in covalent bonding. The alkyl group's tendency to donate electrons derives from this fact.

Electronegativity is defined as the tendency of an atom of an element to draw electrons towards itself in a covalent bond. Electronegativity is a property of an element, and it is the arbitrary Pauling scale that represents how electronegative each element is.

See how hydrogen has been assigned the value #2.20#, whilst carbon is #2.55#? This means that, in a #"C"-"H"# covalent bond, electrons have a greater tendency to be drawn towards the carbon atom; in other words, they spend more time in the carbon atom's local region.

This leads to the carbon atom having an electron excess, and so a partially negative charge (#delta^-#); on the other hand, the hydrogen atom has an electron deficiency and, thus, a partially positive charge (#delta^+#). In this case, we are interested in the former fact.

As a result of the carbon atom's #delta^-# partial charge, it has a repulsive effect on the remaining electron in its valence shell, which encourages the carbon atom to release its electron towards a group with potential for bond formation.

So how does this change with carbon chain length in the alkyl group? As an example, the effect of this is greater in an ethyl group than in a methyl group, because the #delta^-# charge is carried through the chain to the 'uncompleted' carbon atom, so in fact the #delta^-# charge is slightly greater in an ethyl group than in a methyl group.