Ram Charan Mehrotra was born in a middle-class family on 16 February 1922 in Kanpur in the Indian state of Uttar Pradesh to Ram Bharose Mehrotra, a small-time cloth merchant and his homemaker wife, Chameli Devi. He lost both his parents before he turned 10 and had to continue his studies depending on merit scholarships and part-time jobs like private tuition. His primary schooling was at Municipal School, Kanpur and later he joined Christ Church School (present-day Christ Church College, Kanpur) from where he passed the intermediate course, standing first in the state. Joining the University of Allahabad in 1939 for his graduate studies, he completed the course on the strength of three scholarships and passed BSc with Mathematics, Physics and Chemistry as optional subjects. He continued at the university for MSc in chemistry which he passed with first rank in 1943. During this period, he was also involved in student politics in connection with the Quit India Movement of 1942 and had to stay away from studies for four months.
Before starting his formal academic career by joining Allahabad University in 1944 as a member of faculty of inorganic chemistry, Mehrotra worked at Vigyan Kala Bhawan, Daurala, a local learning centre involved in teaching science to prospective young entrepreneurs, for ten months during 1943–44 and was also associated with Vigyan Pragati, a science magazine published by National Institute of Science Communication and Information Resources (NISCAIR) of the Council of Scientific and Industrial Research. He served the university till 1954; in between, he had a short stint of two years at Birkbeck College from 1950 to 1952 as a British Council Fellow and part-time faculty, working with Donald Charlton Bradley; he utilised this period to secure a PhD from the University of London in 1952. He returned to India the same year and resumed his service at Allahabad University when he was offered the position of a reader at Lucknow University in 1954. After serving four years there, he moved to Gorakhpur University in 1958 as a professor where, a year later, he was promoted as the dean of the faculty of science. It was during this time, he served as a member of the Review Committee in Chemistry of the University Grants Commission of India under the chairmanship of T. R. Seshadri, where his colleagues included Asima Chatterjee, a noted chemist.
In 1962, on invitation of Mohan Sinha Mehta, the then vice chancellor of the University of Rajasthan, he took up the post of a professor and head of the newly formed chemistry department and served the institution for two decades. In between, he had a five-year stint as the vice chancellor of Delhi University (from 1974 to 1979) and a short assignment as a UGC National Fellow in December 1979 but on completion of those assignments, he returned to Rajasthan University, where he stayed till 1982; on his move from the university, he was made an emeritus professor. That year, he became associated with the activities of the University Grants Commission, first as the chairman of the Commission on Revision of Pay Scales to Teachers which submitted its report to UGC in 1986. Simultaneously, when the National Commission on Teachers was constituted by the Government of India in 1983 under the chairmanship of D. P. Chattopadhyaya, he was appointed as a member of the Research Advisory Committee. After his assignment with the committee, he took up the chair of the Book Writing Project of the National Council of Educational Research and Training (NCERT) and in 1991, he was appointed as the vice chancellor of the University of Allahabad, a position he held in 1993.
Mehrotra was married to Suman, a Hindi scholar, whom he married in 1944 around the same time when he joined Allahabad University. The couple had two daughters, Rashmi and Shalini and one son, Piyush Mehrotra, in between. He died on 11 July 2004, reportedly due to chronic obstructive pulmonary disease, at the age of 82.