Can I not use my second gen Apple Pencil with iPad Air

You can use Apple Pencil (1st generation) with these iPad models:

• iPad Pro 12.9-inch (1st or 2nd generation)
• iPad Pro 10.5-inch
• iPad Pro 9.7-inch
• iPad Air (3rd generation)
• iPad (7th generation)
• iPad (6th generation)
• iPad mini (5th generation)

You can use Apple Pencil (2nd generation) with these iPad models: 

• iPad Pro 12.9-inch (3rd generation) and later
• iPad Pro 11-inch (1st generation) and later

https://support.apple.com/en-us/HT211029

No you can't. The 2nd gen Apple Pencil works ONLY with iPad Pro 11/12.9 2018 and 2020, all of which have Face ID and charge the pencil via a charging plate on the side of the iPad. Your iPad needs the first generation Apple Pencil. Also, not every generation of iPad Air is compatible with the first generation Apple Pencil. Only iPad Air 3 can use Apple Pencil, this means the first generation and 2nd generation iPad Air cannot use Apple Pencil at all.