Which of the following carbocation will be most stable?
(A) \[{(C{H_3})_3}C\mathop {C{H_2}}\limits^ + \]
(B) \[{(C{H_3})_3}\mathop C\limits^ + \]
(C) \[C{H_3}C{H_2}\mathop C\limits^ + {H_2}\]
(D) \[C{H_3}\mathop C\limits^ + HC{H_2}C{H_3}\]

Hint: The stability of carbocations are decided by the inductive effect of various substituent groups and hyperconjugation. The structure that has substituents that make the positive charge more neutral, will be a more stable structure.


Complete step by step solution:
We know that order of stability of carbocations are Primary < Secondary < Tertiary.
Let’s analyse the stability of all the carbocations given.
A) \[{(C{H_3})_3}C\mathop {C{H_2}}\limits^ + \]
In this molecule, we can see that carbon atom that has positive charge is bonded with one carbon atom and 2 hydrogen atoms. So, this carbocation is a primary carbocation and it will have least stability.
B) \[{(C{H_3})_3}\mathop C\limits^ + \]
Here, the positively charged carbon atom is bonded with three other carbon atoms, so this is a tertiary carbocation and its stability will be higher than primary and secondary carbocations.
C) \[C{H_3}C{H_2}\mathop C\limits^ + {H_2}\]
Here, also the positively charged carbon atom is bonded with only one carbon, so it is a primary carbocation.
D) \[C{H_3}\mathop C\limits^ + HC{H_2}C{H_3}\]
The positively charged carbon atom is bonded with two carbon atoms and one hydrogen atom, so we will call it a secondary carbocation and it will be less stable than tertiary carbocation.
So, we can say that \[{(C{H_3})_3}\mathop C\limits^ + \] will be the most stable carbocation amongst the other carbocations given.

Additional Information:
- If any electron donating group like alkyl group is directly bonded to the carbocation, then it will donate the electron density to the carbocation and will make the carbocation less positive and that will stabilise the carbocation. This is called stabilization by inductive effect.
- If any electron withdrawing group like -COOH group is attached with the carbocation, then it will withdraw the electron density from the carbocation and hence, the carbocation will become more positive in charge, so it will destabilize the carbocation.


Note:
Remember that while giving hyperconjugation structures of a carbocation, the \[\sigma \]- bonds that are \[\beta \] to the carbocations are cleaved to give it stability. Do not think that hydrogens that are directly bound to the carbocation will give contribution in hyperconjugation.