Based on departure/arrive local time, how to know if my flight will be entirely at night?

Both sunset and sunrise move east to west. When it's the wee hours of the morning in Brazil, the sunrise is east of you, in Europe where it's already morning, and headed your way with 3 or 4 hours to reach you if you stood still. Since you're flying east, you're flying in darkness towards the sunrise. Once you reach it, over the Atlantic, you'll be flying in daylight towards the sunset, which is also moving towards you. I am not sure where you will meet that, but perhaps it will be over the ocean as well. The last part of your flight will be in darkness.

The earth is about 24,000 miles in circumference at the equator, so sunrise and sunset move across the earth at 1000 miles per hour there, slower as you get further from it. Your plane will probably be going about 600 miles per hour, so if you're flying straight east, the day (time between sunrise and sunset) will be about 2/3 the normal length and fit entirely into your 13 hours of flight.

You can use Google Earth to calculate this:

• Assume a great circle path
• Search for the start and end locations and draw a great circle between them
• Switch on the day/night function
• Move the date/time slider to the particular time of the flight at departure, then move it to landing

(If I remember, I will add screenshots later today)