Welcome to the Bunnings Workshop community @Alane. It's a pleasure to have you join us and many thanks for your question about building a pergola.
It sounds like our helpful members will need some more information to be able to assist you with your project and question. When we talk about timber spans, it needs to take into account what weight that beam is bearing. What weight will your timber be carrying?
You can research span widths of different dimensions of timber by searching for timber span tables online. Here are some span tables from one of our timber suppliers Hyne. For instance, one of their timbers at 240 x 45mm used as a rafter can only span six meters. Or, a Westbeam 260 x 45mm LVL used as a rafter can span nine meters. However, even though it is coming close, it can then only bear 10kg/m2 of roofing.
A beam might be able to span ten meters, but it won't be able to support much more than its own weight. Ten meters would be an incredibly long length to span unsupported and I would suggest that the pergola design might need to be rethought if it's calling for those type of requirements. Is there anyway you could include a post midway for additional support?