Since you can staff LibraryH3lp using any XMPP/Jabber client, you can staff your service from a mobile device if you so desire. Popular mobile apps include Xabber (Google Play store), IM+ (all platforms), and Trillian (all platforms) but others may work as well.
IMPORTANT! Please be aware that on mobile devices when NOT using AstraChat, operators need to manually switch to Away or Offline within the app when they wish to stop staffing chat. Simply closing (or even uninstalling) the app does not automatically make operators unavailable for chat. With AstraChat, fully exiting the app will disconnect the user from LibraryH3lp's servers.
For Android, the Xabber app is very nice and recommended.
Operators can seamlessly switch between desktop computers and mobile devices if they need -- even during a chat. For example let's say that an operator answers a chat on her mobile device, then decides she wants to continue the chat on her desktop computer with the webclient in Chrome. First, she would need to ensure she is logged into the webclient in Chrome and on Available status. Then she would switch to Away status in the mobile device chat client. The next message from the guest would appear in the webclient on her desktop computer instead of on her mobile device. And the opposite scenario -- taking the chat from webclient to mobile -- works similarly. The basic process is to go to Available status on the device where you want to chat and then go to Away or Offline status on the device/computer where the chat was originally answered.
While your mobile web browser might work in a pinch or for short periods of time, it is not ideal. You really need good push (background) notifications for new chat messages, and that requires a mobile chat app. Push notifications will allow you to do things like allow the device to go idle, lock the device, make another app active, etc, while still receiving reliable alerts of new chat messages. Test your app's notifications thoroughly.
You will also have a difficult time answering questions from your guests using a web browser on a mobile device, because if you need to bring another mobile browser window to the front in the process of answering the question, you might disrupt your network connection to the chat server.
Note that all of these settings probably will not be available in all mobile clients. This is a general listing of possible options across numerous clients.
If available in your app, you'll want to make sure that you have push notifications turned on for any mobile client you install. That way you'll be notified of incoming chats from guests. These clients will have have various settings you can configure for push notifications, including sounds, alerts, and badges. You might have to check in the app's settings AND in your device's general settings for Notifications (especially for iPhone and iPad).