Question

3. Sodium hydroxide (NaOH) reacts with sulfuric acid (H2SO4) to yield sodium sulface (Na2SO4) and water (H2O). The equation for the reaction is wNaOH + H2SO4 →yNa2SO4 + 2H2O, where w, x, y, and z must be chosen to balance the equation. (a) Translate the chemical equation into a system of four linear equations, where each equation balances the number of atoms of a particular element. (b) Express the system as an augmented matrix and solve by Gauss-Jordan elimination. (c) Express the general solution and then interpret in terms of the application. (d) You should have found that there are infinitely many solutions. Explain this result in terms of the chemical equation.

Answer 1

W Na OH + x H so y Na soy + 2 H₂O. a 2 NaOH tQ H Soy > 1 Nq sayt 3 H₂O 2 NaOH + H,soy → Na, soy +2 H, 0. 4 Naola + 2 H₂SO4 2Na, Soy + 4H₂O. → 3 Na, sou + H2O di 6 Na014 + 3H, Soy a) Above footre Equation are balanced Equation { A system of four linear Equation] b) b) Empresas em *3 ay Inpresing system into augmented matrise, Jauss-Jordan ( 2 2 2 1 1 37 1 2 Elimention * d d to 2 L 6 3 36] C, Ry/2 (make the pirot in C, by dividing P, by z] i ! 'lz 3127 6 3 36

SI Eliminate 1 Column (6) 0 - 0 - find the pivot in q in R, L inversing the sign in whole Row Eliminate (2. o o o o

General Johntion solution augment matrix elimination is found from the of grass Jordan (NaOH) x = (1287 / (x4) (H.Soy) *2 =-Xy . Therefore, we found that by varying reaction there are infinitely many solutions for a partialler reaction By using this, we Can use according to our needs. What happens when we double NEOH & Bulfurie accids, we only get more water as by product. So, to get more sodium sulphate (Na, soy) we required times Nach with 2 tones sulphasic acid. With this observation, we can heation obsurse that we get 2 times of Nay soy & y tens of H20.

for better understanding x, replace with a replace with w X replace with a x replace with y Xy replace with a Solution: Test to x- -2 9,42-free. (Product).