Yes, you can send free SMS to a mobile number from Gmail chat. But, this service is limited to US numbers only.
Following are the steps :
1) Login into your Gmail account.
2) Go to ‘Settings’ –> ‘Labs’ tab and Enable ‘Text Messaging (SMS) in Chat’. Same is shown below :
3) Now save this change by clicking on ‘Save changes’.
4) Now, place you mouse pointer on your online contact to whom you want to send SMS. Below window will appear. Click on ‘Video & more’ . Here you will find ‘Send SMS’ option.
5) Click on ‘Send SMS’ and if you have not saved contact’s mobile number earlier then below window will appear(If you already have the number of your contact saved in contact;s detains the it’ll result in the window of step 6). Specify the mobile number in the new window and click on ‘Save’.
6) Now your contact’s mobile number is saved. If you repeat Step 4 then this time a text window will appear on the bottom right corner of your screen where you can type your message and the same will be sent to your friend’s mobile. Below is the same window.
Stay tuned for more.