Here's another problem we're going to do a nice 
chart we have a balance reaction given to us we 
have the Casey value
we start the reaction to put in one mole of die, die 
dined in the two leaders flask and one figure out all 
of the equilibrium concentrations
so using our ice chart method we rewrite the 
reaction
and down the side we fill in the initial change 
equilibrium
this time we're using a Casey which tells us that we 
have to get the unit of molar the to plug into this 
ice chart
molar these moles divided by leaders so one mold 
divided by two leaders
is a starting molar dei of 0.5
that's the only thing we put into this flask we did 
put any Mana, Keidanren they're there for the 
starting amount of that is also zero
because we have zero product we know that the 
product side has to get bigger that site has to be 
the plots
to react inside can only decrease if the product 
side is increasing
the amount that they change again is based on the 
coefficients
coefficient on the left hand side is a wand so we 
were gonna lose acts from the left but on the right 
we're going to gain two acts
at equilibrium you does add down the columns 0.5 
minus acts for the react and
and zero plus two axes just two acts for the product
next we're going to use the value of Kay C
which was given as 3.76 times 10 to the negative 
fifth
in that equals the concentration of the product that 
equilibrium squared divided by the concentration 
of the react and to the first
and if we substitute in from rice chart
the concentration of the product is two acts and 
that has to be squared
the concentration react and his 0.5 -6
ninth race to the first
this equation in Karen is not a perfect square like 
we saw before so we can take the square root and 
make them at any easier
this is an example where we have to use the 
Claudette a formula to solve this equation the first 
thing I'm gonna do is get rid of the fraction
by cross multiplying both sides
and I can get rid of the fraction of the parentheses 
on the right hand side by spinning out two ex client 
is clariden rewriting that as
Forex squared
an imminent bring the 0.5 minus acts over to the 
left
and then I have to distribute the rate of the 
parentheses on the left
and then to get this into the format of the cluttered 
formula I wanna bring all of this over to the same 
side with the Exe squared
so fair rewrite this
I'm gonna have zero equals Forex squared plus
3.76 times and the negative fifth time sects minus
1.88 times 10th and negative fifth
so
now I have this in the correct format I can use the 
clutter formula where X is equal to negative be
plus or minus the square root of the squared lines 
for a C
all over two A
where am I a
B and C are those numbers
so if I make this substitution
immune to come up with two possible answers for 
acts
you plug in all of these values one possibility for 
acts is 2.16
times 10 to the negative third
the other one is -2.17
times 10th the negative third
and if you do your ice charts correctly remember 
acts
represents the increase in this case of the product
that started at zero so we know we can ignore
that negative number because physically and 
negative concentration
doesn't have any meaning so it has to be the 
positive answer
that we're looking for and we're gonna take that 
positive answer for acts
and substitute that back
into the equilibrium role of the ice chart to find eats 
concentration
that's gonna give us the concentration of the react 
and his 0.5 minus acts
0.5 minus acts is 0.4978 and the units are Miller 
the
product is two acts
and it is going to be 4.34 times and the -3 mile
