Question

Which is more stable?
1. ${\left( {C{H_3}} \right)_2} - {C^ \oplus } - C{H_2} - C{H_3}$
2.\[{\left( {C{H_3}} \right)_3} - {C^ \oplus }\]

Answer 1

Hint: The only difference between compound 1 and compound 2 is that compound one contains an ethyl group instead of a methyl group. As ethyl groups are more stabilizing than methyl groups for a carbocation so compound 1 is more stable.

Complete answer:
Let’s start by discussing why tertiary carbocations are more stable.
Though 'stability' is a relative term (carbocations are very reactive, transient species), a tertiary carbocation is more stable than primary and secondary ones; this is due to the electron-releasing effect of its substituent alkyl groups.
Such groups, located around the positive charge-bearing central C atom, release electron density on it, allowing it to be stabilized. This effect is called hyperconjugation and is essentially based on the interaction between a Sigma bond that connects two atoms (e.g. C-H) and a pi bond or antibonding orbital partially occupied (or even empty) on an adjacent atom.
In very simple words, tertiary carbocations are more stable than primary or secondary carbocations because, rather than only one or two methyl groups, they have three methyl groups to distribute their positive charge. To help spread out the positive charge, each methyl group has three hydrogens, which is more effective than just having hydrogen in its place. Of course, the more spread out the positive charge, the more stable your carbocation is going to be.
Now the difference between the two molecules is that molecule 1 contains 1 ethyl group instead of a methyl group. We know that ethyl groups can stabilize carbocation much better than the methyl group as it can spread positive charge much better.
Hence, the following compound is more stable
${\left( {C{H_3}} \right)_2} - {C^ \oplus } - C{H_2} - C{H_3}$

Note:
Carbocation is an ion with a carbon atom that is positively charged. Both carbonate ions were referred to as carbonium ions until the early 1970s. A carbocation is any even-electron cation with a significant partial positive charge on a carbon atom in the present-day definition given by IUPAC.