Algebra Question: Solving for Reaction Constant with Coefficient and Factor

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In summary, the conversation is about trying to find an overall reaction constant and getting stuck on the math behind the problem. The equation being worked on is [Co(H2O)6] = [Co] x (k[H+]/(1+k[H+])) and the goal is to mathematically get to [Co(H2O)6] = [Co] x (1-(1/(1+[H+]k))). The conversation then explores different methods for factoring out the cd term from the numerator in the equation.
  • #1
scrappychic
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I am trying to figure out an overall reaction constant, but I am getting stuck on the math behind the problem. I am at this point in the problem:

[Co(H2O)6] = [Co] x (k[H+]/(1+k[H+]))
And I am trying to mathematically get to
[Co(H2O)6] = [Co] x (1-(1/(1+[H+]k)))

When you ignore the chemistry, the equation is the same as:

a = b x (cd/(1+cd))

going to

a = b x (1-(1/(1+cd)))

How do you factor out the cd from the numerator?

Thanks!
 
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  • #2
It wasn't factored out. (If it was factored out, it would still be there, but outside. :tongue2:)

Try going the other direction: what sort of things can you do to the latter equation?
 
  • #3
So if I work backwards, the step before 1-(1/(1+cd)) could have possibly been
[(1+cd)/(1+cd)] - (1/(1+cd)). What would have led me to that step or is that not the correct step backwards?
 
  • #4
Wait a minute! I think a lightbulb just went off...
 
  • #5
[(1+cd)/(1+cd)] - (1/(1+cd)) This actually reduces back to cd/(1+cd), right? Because the 1-1=0 and cd is the only thing left in the numerator. So what would prompt me to know that I should change cd/(1+cd) into [(1+cd)/(1+cd)] - (1/(1+cd))?
 
  • #6
Well, whether you should change it is another question entirely.

But to figure out how to change it, you can simply use the division algorithm.

You're dividing cd by (cd + 1)...

How many times does (cd + 1) go into cd? 1 time, with remainder -1.

So, cd/(cd+1) = 1 + (-1)/(cd+1)

(when figuring out how many times, you just look at the "biggest" terms -- in this case, we consider any term involving "cd" to be bigger than any term that is just a number)


Another method is to look at it and think "Hrm, I can probably write that as A + B/(cd+1)", and then try to solve the equation "A + B/(cd+1) = cd/(cd+1)"


A third way is to learn how to do what you just did in the opposite direction!
 
Last edited:
  • #7
Thanks so much!
 

What is the definition of algebra?

Algebra is a branch of mathematics that deals with the manipulation and study of symbols and the rules for manipulating these symbols.

What is a variable in algebra?

A variable is a symbol or letter that represents a number or quantity that can vary or change in value.

What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power.

How do you solve a simple algebraic equation?

To solve a simple algebraic equation, you must isolate the variable on one side of the equation by using inverse operations to cancel out any constants or coefficients. The solution is the value of the variable that satisfies the equation.

What is the order of operations in algebra?

The order of operations in algebra is the set of rules that determines the order in which operations should be performed in an expression. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is commonly used to remember the order of operations.

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