[Tipsy]

I am trying to teach myself how to do the PPM calclation. I missed the class cause I was in hospital and really want to catch up before I go back to class.
I read the paragraph in my text and understand that PPM is used to measure very dilute quantities. PPM is 10x -6 and 1Kg of a solution is approximated to be 1 litre (= 1mg/gram)

I know the formula as:

PPM = mass of solute (mg)
          mass of solution in (Kg)

The question I am applying this to is:

A CaCl2 solution has a concentration of 10mg/litre. Express the solutions [CA+2] in PPM

Now, I have no idea where to start. So, this is my thinking.

1. CaCl2 is my solution, Ca+2 is my solute.
2. I need to convert 10mg/litre to kilograms so that is 0.010Kg of CaCl2
3. The weight of Ca = 40.078gm = 0.040078mg (1gm = 1000mg)

4. so, my calculation would be:


0.04
 0.010

= 4 PPM

is this right or am I way off? I am trying to nut this out myself so please be patient with me.       
If I am wrong, can you tell me which of my steps (1, 2. 3 and 4) is incorrect and explain why so i can try again please.

Many Thanks.

[Borek]

You are partially right, but then in some places you are strangely off.

1Kg of a solution is approximated to be 1 litre (= 1mg/gram)

1L of solution is assumed to weight 1kg, that OK, why 1mg/g - I have no idea.

1. CaCl2 is my solution, Ca+2 is my solute.

Convoluted, but probably OK.

2. I need to convert 10mg/litre to kilograms so that is 0.010Kg of CaCl2

From here on you are off.

You have to find mass of Ca in 10 mg of CaCl₂. No need to convert anything to kg. What is molar mass of calcium? What is molar mass of calcium chloride? Can you use these?

[Tipsy]

You are partially right, but then in some places you are strangely off.

1Kg of a solution is approximated to be 1 litre (= 1mg/gram)

1L of solution is assumed to weight 1kg, that OK, why 1mg/g - I have no idea.

1. CaCl2 is my solution, Ca+2 is my solute.

Convoluted, but probably OK.

2. I need to convert 10mg/litre to kilograms so that is 0.010Kg of CaCl2

From here on you are off.

You have to find mass of Ca in 10 mg of CaCl₂. No need to convert anything to kg. What is molar mass of calcium? What is molar mass of calcium chloride? Can you use these?

I ment 1gm per ml (it's 340am here!) sorry. I was just converting it to make sure I was doing my conversions right.

Okay, CaCl₂ = 40.04 +(2x 35.45) = 110.94

molar mass of calcium = 40.04 gm
molar mass of calcium chloride = 70.9gm

then I don't understand what you mean by finding the mass of 10mg Ca in CaCl₂. sorry.

[Borek]

Not mass of 10 mg Ca in CaCl₂ but mass of Ca in 10 mg of CaCl₂.

1 mole of CaCl₂ has mass of 110.94 grams, of that 40.04 is calcium.

110.94 grams of CaCl₂ contains 40.04 g Ca.

10 mg of CaCl₂ contains ... mg Ca.

[Tipsy]

Not mass of 10 mg Ca in CaCl₂ but mass of Ca in 10 mg of CaCl₂.

1 mole of CaCl₂ has mass of 110.94 grams, of that 40.04 is calcium.

110.94 grams of CaCl₂ contains 40.04 g Ca.

10 mg of CaCl₂ contains ... mg Ca.

I can "hear" what you are saying, I can no longer think. I am off to bed, I will be back though later today and hopefully will have a correct answer with the workings out shown!

[Tipsy]

so, my calculation would be
40.04  x 0.01  (convert 10mg to gm)
110.94                x

x= 110.94 x 0.01
          40.04

x = 0.0277gms

so my calculation to this point is

PPM = 27707 < - gms converted to mg
         0.11094    <- CaCl2 = 110.94g converted to kg

PPM = 2503217.955


( I am getting the distinct feeling this is wrong  so am going to give up until you come back please  )

[Borek]

No need to convert anything to grams. Units will cancel out leaving mg (you can easily check it).  Then, your fomula for x is wrong - you are right that you need to use a ratio, but you have switched molar masses of Ca and CaCl₂.

Next steps are off, so we will quietly ignore them.

[Tipsy]

okay....so, my calculation would be
110.94  x 10  
40.04      x      x

x x 110.94 = 40.04 x 10

x = 40.04 x 10
         110.94

x= 3.609

is it right now

[Borek]

x= 3.609

3.609 of what? Please remember about units, as so far you have done strange things with them I can't be sure you get it right this time.

[Tipsy]

x= 3.609

3.609 of what? Please remember about units, as so far you have done strange things with them I can't be sure you get it right this time.

gms of Ca in CaCl2

[Borek]

Do you still remember what you were looking for? How can it be 3.6 g in 10 mg?

Repeat: I will always check my units. I will always check my units. I will always check my units.

[DrCMS]

Note you've changed the molecular weight of Calcium from 40.078g to 40.04g from your first to last posts.  40.078g is correct for calcium and 110.98g for calcium chloride.  It doesn't make a big difference to the final answer which is 3.61.

[Tipsy]

Do you still remember what you were looking for? How can it be 3.6 g in 10 mg?

Repeat: I will always check my units. I will always check my units. I will always check my units.

Borak, you are very patient! Thank you.

Well I guess it would be 3.6 mg in 10mg.

Can you do the calculation for me showing me where the units cancel out. I don't understand what you mean because i thought you needed 2 units of each type to be able to cancel them out.

Thankyou DrCMS, I didn't notice that because i was too hung up on the formula and not looking at my numbers (or units)

[Borek]

x mg / 10 mg = 40 g / 111 g

so

x mg = 40 g / 111 g * 10 mg

40 g / 111 g = 40 / 111 - that's where the units cancel. And you are left with

x mg = 40/111 * 10 mg

(for simplicity I have used 40 & 111 for molar masses instead of more exact ones)

[enahs]

Alternatively. Another way to think of this specific problem.

You said:

and 1Kg of a solution is approximated to be 1 litre

and

PPM = mass of solute (mg)
          mass of solution in (Kg)

and

A CaCl2 solution has a concentration of 10mg/litre. Express the solutions [CA+2] in PPM

So you are already given the solution concentration in PPM. So take a liter of the solution. You have 10 mg of CaCl2, So the answer is just what percentage by mass is the Ca in 10mg CaCl2.

But the other way was good, as you need to know how to do it that way, and keep units.

It is just always nice come test time, if you are worried, and you can recognize two different ways to do the calculation quickly and easily and verify you are correct. Alternatively, the percentage method could be done as a quick estimate in your head as a way to check.

Just throwing it out there.