How far is Puerto Penasco Sonora Mexico to the capital city Mexico city?

Since pre-Columbian times (14th century) it became the political, economic and cultural capital of Mexico. When Spanish conquistadores conquered Mexico in the 16th century, it was deemed natural to...

782.49 kilometres (486.22 miles)

Because it is: Mexico City is the economic, political and cultural capital of the country of Mexico.

I think you mean the town of Dolores, in the Mexican state of Hidalgo, where the cry for the independence of Mexico took place. In that case it is some 317 Km (Some 197 miles) north of Mexico City.

Mexico City became the capital in 1821