Aleks Explanation Calculating equilibrium composition from an equilibrium constant PDF

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Explanation to the Aleks Calculating equilibrium composition from an equilibrium constant....

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QUESTION Suppose a 250.

mL flask is filled with 0.70 mol of NO and 0.10 mol of NO2. The following reaction becomes possible:

NO3 g + NO g

2NO2 g

The equilibrium constant

K for this reaction is 0.847 at the temperature of the flask.

Calculate the equilibrium molarity of

NO2. Round your answer to two decimal places.

EXPLANATION The key to solving an equilibrium composition problem is the connection between the equilibrium molarities of each reactant

K:

and the equilibrium constant

NO2

2

NO3 NO

The equilibrium constant expression is on the left side of this equation.

=K

You can use this equation to calculate K from the equilibrium molarities. But if you know equation "backwards" to calculate the equilibrium molarities.

Kinstead, you can use the

First, set up a reaction table:

NO3

NO2

NO

0

2.8 0.40 Since we're after the equilibrium molarity of NO2, we might as well let 1 −x x − x stand for the change in molarity of NO2 2 1 1 x 2.8 + x 0.40 − x 2 2

initial

1 x 2

change

equilibrium More...

Next, substitute the expressions in the last row of the reaction table for the molarities in the equilibrium constant expression: 2

NO2 NO3 NO

=

0.40 − x 1 x 2

2.8 +

2

1 x 2

=K

Finally, substitute the equilibrium constant for

0.40 − x 1 x 2

2.8 +

K and solve the equation for x:

2

1 x 2

2

0.40 − x = 0.847 2

= 0.847

1 x 2

2.8 +

Here's the equation.

1 x 2

Clear the fraction.

2

0.16 − 0.8x + x = 1.1858x + 0.21175 x

Multiply out both sides.

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2· 0.78825 x = 2.4359, 0.0833

There are two possible values for x.

Although the quadratic formula gives you two values for x, only one is physically reasonable. Which one? Look back at the equilibrium molarities in the equilibrium table. None of them can be negative -- a negative molarity makes no physical sense. In this case, using the first value

x

x = 2.4359

would make at least one equilibrium molarity negative, so using this value for

makes no physical sense.

Now that you know x, go back to the last row of the reaction table and use it to calculate

NO2.

ANSWER

NO2 = 0.32 M

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