The facebook app stays installed and it's greyed out. When I go to redown load it from itunes, it just has an open tab and not a install tab. help

After I upgraded tothe IOS 6 operating system on my iphone 3GS I lost several of my apps. They don't show up anymore. I tried to reinstall them again using itunes, but they just show an "open" tab instead of an "install" tab. When I click open, it brings up the app. I can't figure out how to install the app on my phone again. Help....When I look at my phone the apps are there under settings but not on the phone as an app.