Web Real-Time Communication (WebRTC) combines a set of standards and technologies to enable high-quality audio, video, and auxiliary data exchange in web browsers and mobile applications. It enables peer-to-peer multimedia sessions over IP networks without the need for additional plugins. The Opus codec, which is deployed as the default audio codec for speech and music streaming in WebRTC, supports a wide range of bitrates. This range of bitrates covers narrowband, wideband, and super-wideband up to fullband bandwidths. Users of IP-based telephony always demand high-quality audio. In addition to users’ expectation, their emotional state, content type, and many other psychological factors; network quality of service; and distortions introduced at the end terminals could determine their quality of experience. To measure the quality experienced by the end user for voice transmission service, the E-model standardized in the ITU-T Rec. G.107 (a narrowband version), ITU-T Rec. G.107.1 (a wideband version), and the most recent ITU-T Rec. G.107.2 extension for the super-wideband E-model can be used. In this work, we present a quality of experience model built on the E-model to measure the impact of coding and packet loss to assess the quality perceived by the end user in WebRTC speech applications. Based on the computed Mean Opinion Score, a real-time adaptive codec parameter switching mechanism is used to switch to the most optimum codec bitrate under the present network conditions. We present the evaluation results to show the effectiveness of the proposed approach when compared with the default codec configuration in WebRTC.