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Introduction to reaction rates | Kinetics | AP Chemistry | Khan Academy - YouTube
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- The rate of a chemical reaction
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is defined as the change
in the concentration
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of a reactant or a product
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over the change in time,
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and concentration is in
moles per liter, or molar,
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and time is in seconds.
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So we express the rate
of a chemical reaction
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in molar per second.
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Molar per second sounds a lot like
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meters per second, and that,
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if you remember your physics
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is our unit for velocity.
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So, average velocity is equal to
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the change in x
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over the change in time,
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and so thinking about average velocity
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helps you understand
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the definition for rate
of reaction in chemistry.
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If we look at this applied
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to a very, very simple reaction.
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So we have one reactant, A,
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turning into one product, B.
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Now, let's say at time is equal to 0
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we're starting with an
initial concentration
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of A of 1.00 M,
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and A hasn't turned into B yet.
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So at time is equal to 0,
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the concentration of B is 0.0.
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Let's say we wait two seconds.
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So, we wait two seconds,
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and then we measure
the concentration of A.
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Obviously the concentration of A
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is going to go down
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because A is turning into B.
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Let's say the concentration of A
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turns out to be .98 M.
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So we lost .02 M for
the concentration of A.
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So that turns into,
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since A turns into B after two seconds,
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the concentration of B
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is .02 M.
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Right, because A turned into B.
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So this is our concentration
of B after two seconds.
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If I want to know the average
rate of reaction here,
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we could plug into our definition
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for rate of reaction.
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Change in concentration,
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let's do a change in
concentration of our product,
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over the change in time.
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So, the Rate is equal to the change
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in the concentration of our product,
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that's final concentration
minus initial concentration.
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So the final concentration is 0.02.
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So, we write in here 0.02,
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and from that we subtract
the initial concentration
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of our product, which is 0.0.
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So, 0.02 - 0.0,
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that's all over the change in time.
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That's the final time
minus the initial time,
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so that's 2 - 0.
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So the rate of reaction,
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the average rate of reaction,
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would be equal to 0.02 divided by 2,
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which is 0.01 molar per second.
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So that's our average rate of reaction
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from time is equal to 0
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to time is equal to 2 seconds.
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We could do the same thing
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for A, right,
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so we could,
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instead of defining our rate of reaction
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as the appearance of B,
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we could define our rate of reaction
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as the disappearance of A.
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So the rate would be equal to, right,
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the change in the concentration of A,
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that's the final concentration of A,
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which is 0.98
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minus the initial concentration of A,
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and the initial
concentration of A is 1.00.
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So 0.98 - 1.00,
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and this is all over the final
time minus the initial time,
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so this is over 2 - 0.
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Now this would give us -0.02.
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- 0.02 here,
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over 2,
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and that would give us a
negative rate of reaction,
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but in chemistry, the rate
of reaction is defined
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as a positive quantity.
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So we need a negative sign.
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We need to put a negative sign in here
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because a negative sign gives us
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a positive value for the rate.
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So, now we get 0.02 divided by 2,
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which of course is 0.01
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molar per second.
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So we get a positive value
for the rate of reaction.
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All right, so we calculated
the average rate of reaction
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using the disappearance of A
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and the formation of B,
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and we could make this a
little bit more general.
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We could say that our rate is equal to,
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this would be the change
in the concentration of A
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over the change in time,
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but we need to make sure to
put in our negative sign.
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We put in our negative sign
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to give us a positive value for the rate.
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So the rate is equal to the negative
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change in the concentration of A
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over the change of time,
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and that's equal to, right,
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the change in the concentration of B
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over the change in time,
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and we don't need a negative sign
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because we already saw in
the calculation, right,
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we get a positive value for the rate.
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So, here's two different ways
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to express the rate of our reaction.
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So here, I just wrote it in a
little bit more general terms.
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Let's look at a more complicated reaction.
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Here, we have the balanced equation
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for the decomposition
of dinitrogen pentoxide
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into nitrogen dioxide and oxygen.
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And let's say that oxygen forms
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at a rate of 9 x 10 to the -6 M/s.
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So what is the rate of formation
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of nitrogen dioxide?
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Well, if you look at
the balanced equation,
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for every one mole of oxygen that forms
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four moles of nitrogen dioxide form.
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So we just need to multiply
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the rate of formation of oxygen
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by four,
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and so that gives us,
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that gives us
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3.6 x 10
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to the -5
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Molar per second.
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So, NO2 forms at four times
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the rate of O2.
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What about dinitrogen pentoxide?
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So, N2O5.
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Look at your mole ratios.
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For every one mole of oxygen that forms
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we're losing two moles
of dinitrogen pentoxide.
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So if we're starting with the rate
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of formation of oxygen,
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because our mole ratio is one to two here,
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we need to multiply this by 2,
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and since we're losing
dinitrogen pentoxide,
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we put a negative sign here.
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So this gives us
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- 1.8 x 10 to the -5
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molar per second.
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So, dinitrogen pentoxide disappears
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at twice the rate that oxygen appears.
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All right, let's think about
the rate of our reaction.
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So the rate of our reaction is equal to,
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well, we could just say it's equal
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to the appearance of oxygen, right.
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We could say it's equal to
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9.0 x 10 to the -6 molar per second,
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so we could write that down here.
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The rate is equal to
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the change in the concentration of oxygen
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over the change in time.
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All right, what about if
we wanted to express this
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in terms of the formation
of nitrogen dioxide.
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Well, the formation of nitrogen dioxide
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was 3.6 x 10 to the -5.
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All right, so that's
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3.6 x 10 to the -5.
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So you need to think to yourself,
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what do I need to multiply this number by
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in order to get this number?
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Since this number is four
times the number on the left,
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I need to multiply by one fourth.
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Right, so down here,
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down here if we're
talking about the change
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in the concentration of nitrogen dioxide
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over the change in time,
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to get the rate to be the same,
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we'd have to multiply this by one fourth.
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All right, finally, let's think about,
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let's think about dinitrogen pentoxide.
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So, we said that that was disappearing
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at -1.8 x 10 to the -5.
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So once again, what do I need to multiply
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this number by
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in order to get 9.0 x 10 to the -6?
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Well, this number, right,
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in terms of magnitude
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was twice this number
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so I need to multiply it by one half.
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I need to get rid of the negative sign
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because rates of reaction
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are defined as a positive quantity.
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So I need a negative here.
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So that would give me, right,
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that gives me 9.0 x 10 to the -6.
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So for, I could express my rate,
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if I want to express my rate
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in terms of the disappearance
of dinitrogen pentoxide,
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I'd write the change in N2,
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this would be the change in N2O5
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over the change in time,
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and I need to put a negative
one half here as well.
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All right, so now that we figured out
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how to express our rate,
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we can look at our balanced equation.
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So, over here we had a 2
for dinitrogen pentoxide,
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and notice where the 2 goes here
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for expressing our rate.
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For nitrogen dioxide, right,
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we had a 4 for our coefficient.
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So, the 4 goes in here,
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and for oxygen,
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for oxygen over here, let's use green,
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we had a 1.
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So I could've written 1 over 1,
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just to show you the pattern
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of how to express your rate.
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