System.Net.Sockets.SocketException: A connection attempt failed because the connected party did not properly respond after a period of time

I am implementing Email sending option in my website using below code:

HTML:

<table width="600px" align="center">

       <tr>
            <td> To </td>
            <td> <asp:TextBox ID="txtToMail" runat="server"></asp:TextBox> 
            </td>
        </tr>
        <tr>
            <td> Subject </td>
            <td> <asp:TextBox ID="txtSubject" runat="server" Width="400"></asp:TextBox>
            </td>
        </tr>
        <tr>
            <td> Message </td>
            <td> <asp:TextBox ID="txtMessage" runat="server" TextMode="MultiLine" Width="400px" Height="200px"></asp:TextBox>
            </td>
        </tr>
        <tr>
            <td colspan="2" align="center"> 
                <asp:Button ID="btnSubmit" runat="server" OnClick="btnSubmit_Click" Text="Send" /> 
            </td>
        </tr>
        <tr>
            <td colspan="2">
                 <asp:Label ID="lblMsg" runat="server" ></asp:Label> 
            </td>
        </tr>   
</table>

C#:

using System.Net.Mail;
using System.Net.Security;

protected void btnSubmit_Click(object sender, EventArgs e)
    {
        MailMessage mail = new MailMessage();            // creating object 
        mail.From = new MailAddress("MymailId@gmail.com");   // deciding from which mail add to be send (it can be define at run time by taking value from form through txtbox)
        mail.To.Add(txtToMail.Text);         // adding mail id to which mail is to be send
        mail.Subject = txtSubject.Text;      // deciding subject...
        mail.Body = txtMessage.Text;       // taking mail from form
        SmtpClient smtp = new SmtpClient("smtp.gmail.com", 587);     //setting mail client...it is different for every one
        smtp.Credentials = new System.Net.NetworkCredential("MymailId@gmail.com", "Password"); 
        smtp.EnableSsl = true;  //setting complete mail
        smtp.Send(mail);   //sending mail.....
        lblMsg.Text = "Email has been successfully sent..!!";

    }

but it is giving me error:

System.Net.Sockets.SocketException: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond 173.194.79.109:587

Line:

smtp.Send(mail);

I also tried pinging above mentioned IP i.e., 173.194.79.109.587, and is pingable through my network.

I am unable to understand the cause of error. If any other code is there for e-mail option please do share.

Please help.