session-one/session-one-project-biochem-solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "         O OH\n",
    "H3PO4 (OH P OH) is an example of an oxyacid. \n",
    "The pKa of an any oxyacid can be estimated using Pauling's rules which state:\n",
    "The  pKa  of an oxyacid of general formula  E(OH)q(O)p  is given by pKa=8−5×p.\n",
    "\n",
    "Assign the structural formula for phosphoric accid to an array called PHOSACID. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "PHOSACID =  ['O', 'P', 'OH', 'OH', 'OH']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use the .count(\" \") method to work out the total number of a specific character in a string. Using the .count(\" \") method work out the values for q and p and print the values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of q is 3 and the value of p is 1 .\n"
     ]
    }
   ],
   "source": [
    "q_count = PHOSACID.count('OH')\n",
    "p_count = PHOSACID.count('O')\n",
    "\n",
    "print(\"The value of q is\", q_count, \"and the value of p is\", p_count,\".\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now using the pKa = 8-5xp, workout the pKa of phosphoric acid and print this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pKa of phosphoric acid is 3\n"
     ]
    }
   ],
   "source": [
    "p = p_count\n",
    "ans_pKa = 8 - 5 * p\n",
    "\n",
    "print(\"pKa of phosphoric acid is\", ans_pKa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the import method to import useful python libraries that can help us with various things. We are going to import some libraries that will help with plotting graphs and maths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to use a function called linspace found in the numpy library to generate equally spaced numbers between -5 and 5 and assign these numbers to a variable called x. Then assign the graph 2x+1 to a variable called y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generated equally spaced numbers between -5 and 5 and assigning it to x.\n",
    "x = np.linspace(-5,5)\n",
    "# Assigning our graph to a variable named y.\n",
    "y = 2*x+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now going to plot the graph y = 2x+1 using the matplotlib.pyplot library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using the plt function we are going to plot and then show the graph.\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do more with a plot, we can add colour, grids or we can even plot trickier graphs. \n",
    "\n",
    "The potential energy of two argon atoms separated by a distance r\n",
    "can be roughly given by the following function,$$V(r)= 4\\epsilon[(\\frac{\\sigma}{r})^{12}\\\\-(\\frac{\\sigma}{r})^{6}]$$\n",
    "\n",
    "Using the python libraries we have imported, plot $$f(x)=\\frac{1}{x^{12}}$$ and $$f(x)=-\\frac{1}{x^{6}}$$\n",
    "\n",
    "Remember that both of these graphs have an asymptote, that will cause a zero error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Without defining this function we would keep getting a Divide by Zero \n",
    "# warning because of this graph's asymptote - 1/0^12 is not possible.\n",
    "def f(x):\n",
    "    with np.errstate(divide='ignore', invalid='ignore'):\n",
    "        return 1/x**12\n",
    "    \n",
    "x=np.linspace(-10,10,101)\n",
    "y=f(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    with np.errstate(divide='ignore', invalid='ignore'):\n",
    "        return -(1/x**6)\n",
    "    \n",
    "x=np.linspace(-10,10,101)\n",
    "y=f(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  }
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