1. 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 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

2. So, here’s our chemical equation THe coefficients, w, x, y, and z are
Al2O H2SO4  Al2(SO4) 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 Al2O H2SO4  2 Al2(SO4) H2O
3 Al2O H2SO4  3 Al2(SO4) H2O
1/2 Al2O3 + 3/2 H2SO4  1/2 Al2(SO4)3 + 3/2 H2O

3. Video ID: © 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