## Approximation

Cienna Henry 1J
Posts: 61
Joined: Fri Sep 28, 2018 12:15 am
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### Approximation

When can we use the approximation that allows us to bypass calculating a quadratic?

Jenna Salas 2H
Posts: 30
Joined: Fri Sep 28, 2018 12:22 am

### Re: Approximation

You can use approximation when the concentration you calculate is less five percent of the initial concentration.

David S
Posts: 54
Joined: Fri Sep 28, 2018 12:15 am

### Re: Approximation

You can only use the approximation when equilibrium constant K is notably small. In class, lavelle told us that in general, when K < 10^-3, we can assume the amount of reactant lost to form product (x) is small enough to ignore.

After using this approximation to solve for x, you have to check it using the 5% rule, which is $\frac{change\,in\,\,concentration}{initial\,concentration} < 0.05$

Example:

For the reaction $N_{2(g)}+3H_{2(g)}\rightleftharpoons 2NH_{3(g)}$ with K = 1.64x10^-4 @Temp = 400K
lets pretend initial concentration of N2= 0.1, H2= 0.2, and NH3 = 0.

We know that $K = \frac{[NH_{3}]^{2}}{[N_{2}][H_{2}]^{3}}$

When we set up our Equilibrium equation and ice table, we get $K=\frac{(2x)^{2}}{(0.1-x)(0.2-3x)^{3}}$
That equation looks nasty, but since K is < 10^-3, we can simplify it to $K = \frac{(2x)^{2}}{(0.1)(0.2)^{3}}$

when you solve for x, you want to check that your approximations were valid, so you do:
$\frac{x}{[N_{2}]_{ini}} < 0.05$ and $\frac{3x}{[H_{2}]_{ini}} < 0.05$
As long as those inequalities are true, you are good to go.

Mark 1D
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Joined: Fri Sep 28, 2018 12:18 am

### Re: Approximation

Approximate if it follows 5% rule or equilibrium constant is below x10^-3. But I sometimes use quadratic anyway to double check. :)

BenJohnson1H
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Joined: Fri Sep 28, 2018 12:17 am

### Re: Approximation

Is it acceptable to not round, even when permitted to, on the test?

Hilda Sauceda 3C
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Joined: Fri Sep 28, 2018 12:24 am

### Re: Approximation

yeah i have the same question, if we dont round will it be considered wrong?

Matthew Casillas 1C
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Joined: Fri Sep 28, 2018 12:21 am

### Re: Approximation

Are we allowed to approximate below 10^-4 or 10^-3?

Cienna Henry 1J
Posts: 61
Joined: Fri Sep 28, 2018 12:15 am
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### Re: Approximation

Matthew Casillas 1C wrote:Are we allowed to approximate below 10^-4 or 10^-3?

I think I heard 10^-3