Mochalski was the son of Czeslaw and Lola Mochalski, and was educated at De La Salle College. He received a Bachelor of Law from the University of Sydney before becoming a solicitor; he also worked as a project manager with a public company. He married Deanne in November 1986, with whom he had two children.
In 1980, the Labor member for the state seat of Bankstown, Nick Kearns, died; Mochalski was selected as the Labor candidate for the by-election and was easily elected. He held the seat easily in 1981 and 1984, but in December 1986 he was forced to resign from Parliament, accused of improper conduct over the collapse of the Balanced Property Trust, which he founded and of which he was the director.
- Parliament of New South Wales (2008). "Mr Richard Charles Mochalski". Former Members. Parliament of New South Wales. http://www.parliament.nsw.gov.au/prod/parlment/members.nsf/1fb6ebed995667c2ca256ea100825164/558efdf017cefcc8ca256ce7008026e2?OpenDocument. Retrieved 4 May 2010.
- Green, Antony (2010). "Contests for Bankstown". NSW Election Database. Parliament of New South Wales. http://www.parliament.nsw.gov.au/resources/nswelectionsanalysis/DistrictIndexes/Bankstown.htm. Retrieved 4 May 2010.