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

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:

$\displaystyle \begin{tabular}{ccccccccc} & A & + & B & = & 0.3 & & & \\ - & A & & & & & - & A & \\ \hline & & & B & = & 0.3 & - & A & (\mbox{Equation 1})\end{tabular}$

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

$\displaystyle 0.616 \times B = \dfrac{A}{B}\times B$

Since $\displaystyle B = \dfrac{B}{1}$, we can rewrite the equation: $\displaystyle 0.616 \times B = \dfrac{A}{B} \times \dfrac{B}{1}$.

This simplifies to $\displaystyle 0.616B = A (\mbox{Equation 2})$.

So, now we have two different equations (Equation 1 and Equation 2):

$\displaystyle B = 0.3 - A$

$\displaystyle 0.616B = A$

The first equation tells us that wherever we see $\displaystyle B$, we can replace that by $\displaystyle (0.3 - A)$ because the two values are equal. So, in the second equation, we will make this replacement:

$\displaystyle 0.616(0.3-A) = A$. That is where the book writes $\displaystyle 0.616(0.3-[HPO4]) = [HPO4]$ (This is why I assume that $\displaystyle A = [HPO4]$).

Now, on the left hand side of the equation, we need to distribute the multiplication. So, we have:

$\displaystyle 0.616 \times 0.3 - 0.616 A = A$

This works out to $\displaystyle 0.185 - 0.616 A = A$ (again, replace $\displaystyle A$ by $\displaystyle [HPO4]$ and you have what the book wrote).

Now, we will add $\displaystyle 0.616A$ to both sides of the equation:

$\displaystyle 0.185 -\sout{0.616A} + \sout{0.616A} = A + 0.616A$

$\displaystyle 0.185 = 1.616A$ (replace $\displaystyle A$ by $\displaystyle [HPO4]$ and you again have what you saw in the book).

Finally, divide both sides of the equation by 1.616 to get $\displaystyle 0.114 = A$. Now that you have $\displaystyle A$, you can plug that into (Equation 1) to get $\displaystyle B = 0.3 - A = 0.3 - 0.114 = 0.186$.

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.

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?

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

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!

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)

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:

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

a picture to demonstrate:

http://s23.postimg.org/tlgupje97/distributive.png

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)

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

Ah thanks, that explains the concept well.