Stepped adsorption isotherms with desorption hysteresis were measured for nitrogen, argon, ethane, carbon dioxide, and methane at pressures up to 17 MPa on zeolitic imidazolate framework-7 (ZIF-7) using a gravimetric sorption analyzer. Such stepped sorption isotherms have not been previously reported for nitrogen or argon on ZIF-7, and required the application of pressures as high as 15 MPa to trigger the ZIF-7 structural phase transition at temperatures around 360 K. The stepped hysteretic sorption isotherms measured for carbon dioxide, methane, and ethane were consistent with previous observations reported in the literature. To correlate these stepped hysteretic sorption isotherms, a semi-empirical model was developed by combining a three-parameter Langmuir equation to describe the Type I aspect of the isotherm, with a model designed to describe the temperature-dependent ZIF-7 structural phase transition. Excellent fits of the combined adsorption and desorption branches were achieved by adjusting nine parameters in the temperature-dependent model, with root-mean-square deviations within 2.5 % of the highest measured adsorption capacity. Each parameter of the new semi-empirical model has a physical basis, allowing them to be estimated or compared independently.