Yulia V. Tymoshenko, once one of Ukraine’s most powerful and popular politicians, was sentenced on Tuesday to seven years in prison, the culmination of a politically charged trial that could presage the end of the country’s short and often raucous experiment with democracy.

The sentence was the maximum demanded by prosecutors on charges that Ms. Tymoshenko had harmed Ukraine’s interests when, as prime minister, she carried out negotiations with Russia in 2009 over the price of natural gas. Her supporters and many Western officials have insisted that her actions could hardly have amounted to a crime.