Problem 1: The following formula [3]. The elements are Si, Al, Fe, Mg, K, H and
ID: 2261979 • Letter: P
Question
Problem 1: The following formula [3]. The elements are Si, Al, Fe, Mg, K, H and O. The species are qu quartz (SiO2) si - sillimanite (Al2SiO5) Kf - K feldspar (KAlSi308) st -steam (H20) al - almandine (Fe3Al2Si3012) py - pyrope (Mg3Al2Si3012) an annite (KFe3SigAIOo(OH)2) ph - phlogopite (KMg3Si3AlO10(OH)2) Fec = Fe-cordierite (Fe2AI4Si:08) Mgc - Mg-cordierite (Mg2Al4Si;018). matrix occurs in a chemical system given by a rock sample Thus, the formula matrix qu si Kf st al py an ph Fec Mgc Si 1 1 3 0 33 335 Al 0 21 0 2 2 1 4 Fe 0 00 0 30 3 02 4 A=Mg| 0 0 0 0 0 3 0 3 2 K0 01 00 0 1 10 H0 00 20 0 220 O 2 5 8 112 12 12 12 18 18 (i) Determine possible reactions for this system (ii) Is there a fixed ratio of molar amounts of the elements in every possible sample composed of species from this systemExplanation / Answer
(i.)MATLAB code to calculate eigen values:
clc;clear all;close all;
A=[1 1 3 0 3 3 3 3 5 5;0 2 1 0 2 2 1 1 4 4;0 0 0 0 3 0 3 0 2 0;0 0 0 0 0 3 0 3 0 2;0 0 1 0 0 0 1 1 0 0;0 0 0 2 0 0 2 2 0 0;2 5 8 1 12 12 12 12 18 18;0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0];
[v,d]=eig(A);
display(v);
Result:
Thus,the first 7 rows gives the co-efficients for the possible reactions for this system.
The last three rows are obtained as the matrix A is truncated by 3 rows of [0 0 0 0 0 0 0 0 0 0]'s in order to obtain a square matrix.
(ii.) The ratio of molar amounts of the elements in every possible sample composed of species from this system , are dynamic and is not fixed, As let us consider the qu,si,Kf,st,al,py,an,ph,Fec,Mgc all the ten species are mixed in ration of a1:a2:a3:a4:a5:a6:a7:a8:a9:a10 which results in the ratio of molar amounts of the elements as Si,Al,Fe,Mg,K,H,O as (a1+a2+3*a3+3*a5+3*a6+3*a7+3*a8+5*a9+5*a10):(2*a2+a3+2*a5+2*a6+a7+a8+4*a9+4*a10):(3*a5+3*a7+2*a9):(3*a6+3*a8+2*a10):(a3+a7+a8):(2*a4+2*a7+2*a8):(2*a1+5*a2+8*a3+a4+12*a5+12*a6+12*a7+12*a8+18*a9+18*a10) , which is not going to be constatn for different proportions of species mixed.
-0.25047 0.249642 -0.35616 0.478821 0.666667 0.451368 -0.36491 0.156327 -0.23067 0.206828 -0.09891 0.178671 0.04481 0.306141 0.333333 -0.85208 0.182664 0.078164 -0.35328 -0.09097 -0.17807 -0.40414 0.814415 -0.35017 -0.33333 0.220492 -0.3945 -0.07816 -0.28125 -0.42739 -0.02011 0.437444 0.047346 -0.43962 -0.33333 0.04605 0.630236 -0.07816 -0.28125 -0.42739 -0.06599 -0.03205 -0.45203 -0.41198 -0.33333 0.134468 -0.21183 0.448546 -0.59851 -0.42739 -0.11328 -0.5285 -0.02763 0.030675 -4.88E-16 0.021657 0.477675 -0.52671 -7.93E-17 -0.25918 -0.93711 0.520317 -0.02317 0.43641 0.333333 -0.03077 -0.08717 -0.44855 0.281246 0.427386 0 0 0 0 0 0 0 0.52671 0 0 0 0 0 0 0 0 0 0 0.475895 0 0 0 0 0 0 0 0 0 0 0.388766