Which of the following words would appear second in the English dictionary when they are arranged in proper alphabetical order?

Let's align and compare the words letter-by-letter to determine their alphabetical dictionary sequence:
All words start with N $\to$ a. Let's compare starting from the $3^{\text{rd}}$ letter:

1. Narrate (starts with n-a-r...)
2. National (starts with n-a-t-i...)
3. Natural (starts with n-a-t-u...)
4. Maps (starts with n-a-v...)

Sorting them in ascending order based on alphabetical ranks (r comes before t, i comes before u, and t comes before v):

* $1^{\text{st}}$ word: Narrate
* $2^{\text{nd}}$ word: National
* $3^{\text{rd}}$ word: Natural
* $4^{\text{th}}$ word: Navigate

Thus, the word that appears second is 'National'.