To optimize learning experience and improve learning performance, current virtual experimental systems usually assist students with stepwise guidance before operations and feedback after them. However, stepwise and excessive guidance can lead to student overreliance, while late feedback cannot avoid potential errors during experimental learning. Meanwhile, some studies indicate that providing experimental guidance and feedback in the early stage of experimental tasks is more effective for knowledge transfer and beneficial for students. Therefore, this study aims to investigate the effects of providing precise experimental guidance and feedback via operation intention prediction in the early stage of experimental tasks. Specifically, an operation intention prediction method based on hand--eye coordination is proposed for the experimental scenario, and first applied to a virtual chemistry experimental learning environment containing complex operation context, assuming that people typically focus their gaze on an object before reaching for it. Guidance and feedback are then adaptively and precisely provided based on the prediction results, thus avoiding potential errors and improving subjective satisfaction. A mixed reality (MR) experimental system is further developed using the proposed method and two evaluation experiments were conducted, with all participants being non-chemistry major university students aged 20 to 25. An accuracy evaluation involving 19 participants demonstrates that the method correctly prompts users' errors in a timely manner with an accuracy of 91.2%, indicating that based on the hand--eye coordination theory, operation intentions can be accurately predicted to provide guidance and feedback. Additionally, a user experiment involving 30 participants investigated the impact of the MR system on learning performance and user subjective satisfaction in chemistry experiments. Results indicated that, compared to the web-based experimental system NOBOOK, although the MR system did not show a significant difference in overall learning performance, it achieved higher average scores among high prior knowledge students, which may be attributed to different learning strategies. High prior knowledge students can better understand guidance information and reduce extraneous cognitive load. Furthermore, the MR system demonstrated significantly better subjective satisfaction in four aspects including user experience, learning content, learning motivation, and practicality. Students generally believed that the MR system could better assist them in learning and hoped it would be used in other learning scenarios. Since the learning assistance is provided based on the individual's hand and eye movement, it can be further applied to personalized education, even for real experiments.