Problem 5 [5 marks] The Rachford-Rice algorithm is commonly used to perform isothermal flash calculations vapour-liquid mixtures. If temperature and pressure are known, then the algorithm is normally used to determine the fraction of the system that exists in the vapour phase (fr) and the composition (mole fractions) of the vapour and liquid phases. The Rachford-Rice equation is where fv is the fraction of the system that exists in the vapour phase, z is the overall mole fraction of component i, K, is the distribution coefficient of component i, and C is the number of chemical species. If zi and Ki are known (or calculated based on temperature and pressure), then this equation can be solved for fv. Since fy must be between 0 and 1, the root of the equation is naturally bounded. Additionally, the function is generally well-behaved in this range, and therefore Newton's method is a good option for determining the root. The derivative of the function is: 1-K Once fi has been determined, the vapour and liquid mole fractions can be determined using: (3a) (3b) where x, is the liquid phase mole fraction of component k and y is the vapour phase mole fraction of component i Consider a system that contains seven components, and has the following overall mole fractions and distribution coefficients Component Component 0.0079 0.1321 0.0849 0.269 Ki 16.2 5.2 2.6 1.98 0.0589 0.1321 0.3151 Ki 0.91 0.72 0.28 4 Write a MATLAB script that uses Newton's method to solve for fr for this system to a tolerance of 10. The script should print the resulting fr value and a table of x and yi values to the command prompt. You do not have to write Newton's method in a separate function for this problem, but may do so if you wish. Submit your MATLAB script, along with explanations of your procedures