A method of a hydrocarbon product and ammonia comprises introducing C2H6 to a positive electrode of an electrochemical cell comprising the positive electrode, a negative electrode, and a proton-conducting membrane between the positive electrode and the negative electrode. The proton-conducting membrane comprising an electrolyte material having an ionic conductivity greater than or equal to about 10−2 S/cm at one or more temperatures within a range of from about 150° C. to about 600° C. N2 is introduced to the negative electrode of the electrochemical cell. A potential difference is applied between the positive electrode and the negative electrode of the electrochemical cell. A system for co-producing higher hydrocarbons and NH3, and an electrochemical cell are also described.