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A 19-25 25-17 25-22 25-23 victory at the Maracanazinho saw China win the event for the first time since 2004.
Errors from Serbia proved crucial, as they made 27 to China's 17 to slump to defeat in one hour, 37 minutes.
This marked a first ever women's volleyball medal for Serbia, while only Russia (four) have won more gold medals than China.
The United States, runners-up in Beijing and London, took out the bronze medal thanks to a 25-23 25-27 25-22 25-19 victory over Netherlands.
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