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Math Help - Hi, im terrible at maths and need a dumbed down explanation of something simple

  1. #1
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    Hi, im terrible at maths and need a dumbed down explanation of something simple

    Hi guys, im working through some chemistry problems and i have zero math ability. Part of my problem requires me to Work out two values
    for e.g

    0.616 = A / B
    A + B = 0.3

    Its to work out the concentrations of an acid and a base in a chemical reaction. This is the part im stuck on. I know A divided by B = 0.616 and i know that if you add A + B together it comes to 0.3
    Is there a method to work this out. In the book it gives this but i don't under stand where it gets some of the numbers from.

    HPO4 (is just the chemical name)

    0.616 x (0.3m -[HPO4] = [HPO4])
    0.185 - 0.616 x [HPO4] = [HPO4]
    0.185 = 1.616 x [HPO4]
    0.114m = HPO4

    So A = 0.114 and B = 0.186

    I dont understand what they are doing to get the concentration....Can someone explain in simple terms?

    Thanks
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  2. #2
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    I am going to make some assumptions here. A is the concentration of the HPO4 and B is the concentration of something else. Let's start with the equation A+B = 0.3 and subtract A from both sides:
    \begin{tabular}{ccccccccc} & A & + & B & = & 0.3 &   & &  \\ - & A &   &   &  & & - & A & \\ \hline & & & B & = & 0.3 & - & A & (\mbox{Equation 1})\end{tabular}

    Next, for the equation 0.616 = \dfrac{A}{B}, we will multiply both sides of the equation by B:
    0.616 \times B = \dfrac{A}{B}\times B

    Since B = \dfrac{B}{1}, we can rewrite the equation: 0.616 \times B = \dfrac{A}{B} \times \dfrac{B}{1}.
    This simplifies to 0.616B = A (\mbox{Equation 2}).

    So, now we have two different equations (Equation 1 and Equation 2):
    B = 0.3 - A
    0.616B = A

    The first equation tells us that wherever we see B, we can replace that by (0.3 - A) because the two values are equal. So, in the second equation, we will make this replacement:
    0.616(0.3-A) = A. That is where the book writes 0.616(0.3-[HPO4]) = [HPO4] (This is why I assume that A = [HPO4]).
    Now, on the left hand side of the equation, we need to distribute the multiplication. So, we have:
    0.616 \times 0.3 - 0.616 A = A
    This works out to 0.185 - 0.616 A = A (again, replace A by [HPO4] and you have what the book wrote).
    Now, we will add 0.616A to both sides of the equation:
    0.185 -\sout{0.616A} + \sout{0.616A} = A + 0.616A
    0.185 = 1.616A (replace A by [HPO4] and you again have what you saw in the book).

    Finally, divide both sides of the equation by 1.616 to get 0.114 = A. Now that you have A, you can plug that into (Equation 1) to get B = 0.3 - A = 0.3 - 0.114 = 0.186.
    Last edited by SlipEternal; October 1st 2013 at 12:13 PM.
    Thanks from topsquark
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  3. #3
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    You have explained this amazingly, yet i still am struggling to understand it. Thats just a reflection on my awful maths tho. Thanks alot for this, i suspect if i read over it enough everything will become clear.
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  4. #4
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    Hi, sorry i am just reading over it, i have a few questions.

    Where did the 1.616A come from? You had 0.185 - 0.616A + 0.616A = A + 0.616A Then that equals 0.185 = 1.616A - Where did that 1 come from?
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  5. #5
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    From A + 0.616A
    You can factor out the A so it becomes A(1+0.616)
    Hence 1.616A
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  6. #6
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    Thanks, Again im a maths noob, is that a general rule?
    Everytime i have

    A + num x A

    Can i factor out the A's and put a one in front? Seems weird!
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  7. #7
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    Well A is equal to 1 x A
    So A + num x A= 1 x A + num x A= A(1+num)
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  8. #8
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    Are you familiar with the distributive property?

    for any numbers a, b, and c:

    a \cdot (b + c) = a \cdot b + a \cdot c

    a picture to demonstrate:



    The area of the left rectangle, a*b, plus the area of the right rectangle, a*c, is equal to the entire big rectangle, a * (b+c)
    Last edited by SworD; October 1st 2013 at 06:01 PM.
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  9. #9
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    Re: Hi, im terrible at maths and need a dumbed down explanation of something simple

    Ah thanks, that explains the concept well.
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