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    "# 2.4 – Degrees of Freedom for Reactive Systems\n",
    "\n",
    "---"
   ]
  },
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    "## 2.4.0 – Learning Objectives\n",
    "\n",
    "By the end of this section you should be able to:\n",
    "\n",
    "1. Calculate degrees of freedom using extent of reaction or atomic species for reactive systems\n",
    "\n",
    "---"
   ]
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    "## 2.4.1 – Introduction \n",
    "\n",
    "As you learned in Module - 1, degrees of freedom(DOF) can save you precious time and resources. It is very improtant to perform a DOF analysis before calculating the solution to any problem.\n",
    "\n",
    "---"
   ]
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    "## 2.4.2 – Degrees of Freedom for Extent of Reaction\n",
    "\n",
    "The DOF of extent of reaction can be calculated by using the following equation:\n",
    "\n",
    "$$ DOF = \\text{# of unknown varibles} + \\text{# of independant reactions} - \\text{# of independant reactive species} - \\text{# of independant nonreactive species} - \\text{# of other equations relating unknown varibles} $$\n",
    "\n",
    "This will equation will inform you if the problem is solvable.\n",
    "\n",
    "---"
   ]
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    "## 2.4.3 – Degrees of Freedom for Atomic Species Balances\n",
    "\n",
    "The DOF of atomic species balances can be calculated by using the following equation:\n",
    "\n",
    "$$ DOF = \\text{# of unknown varibles} - \\text{# of independant atomic species balances} - \\text{# of molecular balances on independent nonreactive species} - \\text{# of other equations relating unknown varibles} $$\n",
    "\n",
    "This will equation will inform you if the problem is solvable.\n",
    "\n",
    "---"
   ]
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