Absolutely positively don't use anywhere close to 4 GB of memory. Most people use 32-bit browsers, so the browser couldn't support 4 GB anyway :)
On a more practical note, remember that the more memory you take up, the slower your app will usually run. Today's Intel/AMD (I don't know about ARM) processors access registers about 100 times faster than accessing memory that isn't in cache, so if you use a lot of memory you will cause thrashing, which will slow down your application dramatically.
So, assuming that you want users for your social network, you should try to design your website to work well on as many machines as possible. Millions and millions of people are still using Windows XP machines that are 5+ years old. These machines might have as little as 512 MB of RAM, so if you are using a few hundred megabytes, you can thrash all of memory rather than just processor cache, as the kernel keeps swapping out pages that you want to use. So as a rule of thumb I would recommend staying below 150-200 MB of memory. GMail takes up ~100MB of memory on Chrome for Linux, so I think that keeping up with GMail is a reasonable goal.
Another benefit of keeping memory usage relatively low is that your users can more easily view your site on a smartphone. An iPhone 3GS (there are still a lot of them in use) has only 256 MB of RAM, so staying below 200 MB in your website makes it easier for a smartphone user to load your site without having to kill processes indiscriminately.
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