{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu-pro","formal_name":"MMLU-Pro","introduction":"MMLU-Pro rebuilds MMLU with ten answer options instead of four and removes items that no longer separate models. Questions span fourteen academic and professional subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"aa6f47cd-89c6-54ba-a67a-e6387023c330","task_key":"default--test--4569","task_revision_id":"1","upstream_id":"4569","short_description":"The mean ionic activity coefficient of an electrolyte in a dilute solution is…","config":"default","split":"test","body":"{\"category\":\"chemistry\",\"options\":\"['\\\\\\\\gamma_1 = e[{(Av^2) / (3n_1)} m^3/2]', '\\\\\\\\gamma_1 = e[{(Av^2) / (2n_1)} m^3/2]', '\\\\\\\\gamma_1 = e[{(Av) / (3n_1)} m^3/2]', '\\\\\\\\gamma_1 = e[{(Av) / (3n_1^2)} m^3/2]', '\\\\\\\\gamma_1 = [{(Av) / (3n_1)} m^3/2]', '\\\\\\\\gamma_1 = [{(Av^2) / (3n_1)} m^3/2]', '\\\\\\\\gamma_1 = [{(A) / (n_1v)} m^3/2]', '\\\\\\\\gamma_1 = e[{(A) / (2n_1v^2)} m^3/2]', '\\\\\\\\gamma_1 = e[{(A) / (3n_1v)} m^3/2]', '\\\\\\\\gamma_1 = [{(Av) / (2n_1)} m^3/2]']\",\"question\":\"The mean ionic activity coefficient of an electrolyte in a dilute solution is given approximately by ln \\\\gamma_\\\\pm = - A\\\\surd(m) where m is the molality and A is a constant. Using the Gibbs-Duhem equation find the activity coefficient \\\\gamma_1 of the solvent in this dilute solution in terms of A, m, and constants characteristic of the solvent and solute. Ob-serve that ln X_1 = ln [(n_1) / (n_1 + mv)] = ln [(1) / {(1 + mv) / n_1}] \\\\approx - [(mv) / (n_1)] where v is the number of ions in the formula (for example v = 2 for NaCl) and n_1 is the number of moles of solvent in 1000 g of solvent. All quantities except \\\\gamma_1 , the un-known, can thus be expressed in terms of the variable m.\",\"src\":\"stemez-PhysicalChemistry\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}