If w=1, then which of these is true? A. y=2, B. z=3, C. x=6 QUESTION: Consider the following chemical equation where coefficients are represented by the letters w,x,y, and z: w Al2O3 + x H2SO4  y Al2(SO4)3 + z H2O If w=1, then which of these is true? A. y=2, B. z=3, C. x=6 In a chemical equation, number of atoms must be the same on both sides of the arrow, for each element. Counting atoms: coefficient x subscript. ELEMENT LEFT RIGHT Al 2w 2y O 3w + 4x 12y + z H 2x 2z S x 3y Consider the following chemical equation where coefficients are represented by the letters w,x,y, and z: w Al2O3 + x HCl  y AlCl3 + z H2O If w=1, then which of these is not true? A. y=2, B. z=2, C. x=6 PAUSE CLICK In a chemical equation, the number of atoms must be the same on both sides of the arrow, for each element. To count atoms, we simply multiply the coefficient by the subscript. Let’s set up a table that will allow us to relate the values of the coefficients w, x, y, and z. We find aluminum in aluminum oxide on the left. HIGHLIGHT Al in Al2O3 THe coefficient of aluminum oxide is w. HIGHLIGHT coefficient and the subscript of aluminum in aluminum oxide is 2. HIGHLIGHT subscript Therefore, the number of Al atoms on the left is equal to w times 2, ... or 2w HIGHLIGHT 2w in table On the right-hand side, we see that the aluminum is found in aluminum sulfate. HIGHLIGHT Al in Al2(SO4)3 The coefficient of aluminum sulfate is y. HIGHLIGHT y and the subscript of aluminum in aluminum sulfate is 2. Therefore, the number of Al atoms on the right is equal to y times 2, ... or 2y. HIGHLIGHT 2y in table Let’s take a look at oxygen. We find in in both aluminum sulfate and sulfuric acid on the left side HIGHLIGHT O in Al2O3 and O in H2SO4 So the total number of oxygen atoms on the left is equal to 3w + 4x. HIGHLIGHT 3w+4x in the table. The 3w comes from Aluminum oxide. The coefficient of aluminum oxide is w. and the subscript of oxygen in aluminum oxide is 3. Similarly, the 4x comes from sulfuric acid. The coefficient of sulfuric acid is x. and the subscript of oxygen in sulfuric acid is 4. On the right hand side, the number of oxygen atom 12y + z. HIGHLIGHT 12y+z The 12y comes from aluminum sulfate. And the total subscript of oxygen in aluminum sulfate is 12. THere are three sulfates in aluminum sulfate HIGHLIGHT 3 in Al2(SO4)3 and there are four oxygen atoms in each sulfate HIGHLIGHT 4 in Al2(SO4)3 ... 3 times 4 equals 12. You should be able to derive the formulas for the rest of the table. Let’s see what happens if we assign a value of one to w. So 2w equals 2 times 1, or 2. TEXT “ = 2(1) = 2” next to 2w From the table, we can see that for Aluminum to be balanced, 2w must be equal to 2y Therefore, 2y must be also be equal to 2 TEXT “ = 2” next to 2y IF 2y equals 2, then y must be equal to 1. Choice A is wrong. CROSS OUT choice A If w equals 1, then y equals 1, not 2. OK. At this point, we know w and y are both equal to one. What else can we determine? PAUSE 2 seconds Here... HIGHLIGHT 3y the number of sulfur atoms on the right is 3y. We know that y is equal to 1.... So 3y is equal to 3. TEXT “ = 3(1) = 3 “ next to 3y In order for chemical equation to be balanced HIGHLIGHT S the number of sulfur atoms on the left must equal the number on the right. The number on the left is x. HIGHLIGHT x THerefore, x must be equal to 3. TEXT “ = 3 “ next to x Therefore, choice C is also wrong. If w equals 1, then x equals 3, not 6. THe correct answer must be choice B. Let’s verify that z is, in fact, equal to 3. Let’s seem what else we can identify in the table. We can see that the number of hydrogen atoms on the left is 2x. HIGHLIGHT 2x We already know that x is equal to 3. Therefore, 2x is equal to 2 times 3, or 6. TEXT “ = 2(3) = 6” In order for the chemical equation to be balanced, the number of hydrogen atoms on the right must also be equal to 6. HIGHLIGHT 2z In other words, 2z must be equal to 6 TEXT “ = 6 “ next to 2z If 2 times z is equal to 6, then z itself must be equal to 3. Thus, the correct answer is B. If w=1, then z is equal to 3. Let’s verify that oxygen is also balanced. The number of oxygen atoms on the left is 15 TEXT “3(1) + 4(3) = 15” ...3w + 4x is equal to 3 times 1 plus 4 times 3, or 15 The number of oxygen atoms on the right is also 15. TEXT “12(1) + 3 = 15” ...12y + z is equal to 12 times 1 plus 3, or 15. CONTINUED ON NEXT PAGE y=1 z=3 x=3

So, here’s our chemical equation THe coefficients, w, x, y, and z are Al2O3 + 3 H2SO4  Al2(SO4)3 + 3 H2O w x y z 1 3 2 6 9 1 / 2 3 / 2 3 /2 So, here’s our chemical equation THe coefficients, w, x, y, and z are 1 CALLOUT “Implied 1” ...3 HIGHLIGHT 3 ...1 ...and 3 HIGHLIGHT 3. Note that this is just one way of balancing the equation. We can multiply all the coefficients by the same number and get another set of valid coefficients. CLICK For example, if we multiply all our coefficients by 2.... Instead of 1, 3, 1, and 3.... HIGHLIGHT row 2 of table (2,6,2,6) we get 2, 6, 2, and 6 HIGHLIGHT row 3 of table CLICK This is also a balanced equation. Or, if we multiply all the coefficients by 3... HIGHLIGHT Row 4 of table (3,9,3,9) we get coefficients of 3, 9, 3, and 9 CLICK This is also a balanced equation. We can even use fraction coefficients... For example, we can multiply all coefficients by ½. HIGHLIGHT Row 5 of table (1/2, 3/2, ½, 3/2) We can assume ANY value for any one of the coefficients, .... then we can figure out all the other coefficients. It is, of course, convenient to deal with small whole numbers, so that’s we did here. CLICK PAUSE END RECORDING 2 Al2O3 + 6 H2SO4  2 Al2(SO4)3 + 6 H2O 3 Al2O3 + 9 H2SO4  3 Al2(SO4)3 + 9 H2O 1/2 Al2O3 + 3/2 H2SO4  1/2 Al2(SO4)3 + 3/2 H2O

Video ID: 1-31-3 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08