{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"c08a82bc-19d9-587d-b75f-a8a2e99eb167","task_key":"olympiad--test--3d762ba1~2d3958~2d453b~2db34e~2dfe24c2822994","task_revision_id":"1","upstream_id":"3d762ba1-3958-453b-b34e-fe24c2822994","short_description":"When considering enzyme kinetics, there are some cases when as the substrate…","config":"olympiad","split":"test","body":"{\"problem\":\"When considering enzyme kinetics, there are some cases when as the substrate concentration increases, the initial rate of the enzymatic reaction passes through a maximum and then decreases. This type of relationship can often be described by the formation of an SES complex that has no enzymatic activity. The following reactions demonstrate this dependence in a given system:\\n\\n`\\\\( E + S \\\\leftrightharpoons ES \\\\)`  with equilibrium constant `\\\\( K_s \\\\)` \\n\\n`\\\\( ES + S \\\\leftrightharpoons  SES \\\\)`  with equilibrium constant `\\\\( J_s \\\\)` \\n\\n`\\\\( ES \\\\rightarrow E + P \\\\)`  with rate constant `\\\\( k \\\\)` \\n\\nAlso make the following assumptions:\\n\\na) \\\\[`\\\\( S]_0 >> [E]_0 \\\\)`, where `\\\\( [E]_0  \\\\)` and `\\\\( [S]_0  \\\\)` represent the initial concentration of enzymatic sites and substrates respectively, when no enzymatic sites are occupied by substrates.\\n\\nb) all equilibria have been established\\n\\nc) initial conditions are considered, `\\\\( [S] = [S]_0  \\\\)` \\n\\nGiven that the system follows the general form of the michaelis-menten equation which states that `\\\\( v_0 = \\\\frac{k_{cat}[E]_0[S]}{K_M + [S]}  \\\\)` , where `\\\\( v_o \\\\)` represents the initial rate of the enzymatic reaction, determine the corresponding `\\\\( K_M  \\\\)` for the system described, in terms of `\\\\( [S] \\\\)`  and given constants.\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"chemistry\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}