EK Chem Formula Error (parts per million)

[Testosterone]

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I think one of the definitions in the Chemistry book is wrong. I

They define parts per million with the following formula

ppm = mass solute/ total mass solution * 10^6

Shouldn't it be ppm= mass solute / total mass solution * 10^-6?

 

[milski]

They have it right. ppm is much smaller unit. For example, 3 ppm is 3x10^-6 mass ratio. Or 3 ppm = 3x10^-6 mass ratio * 10^6 ppm/mass ratio.

 

[shaboobly]

instead of remembering that extra factor i just remember that ppm is (mg solute/L solution)

 

[Testosterone]

instead of remembering that extra factor i just remember that ppm is (mg solute/L solution)

This is exactly why I am confused. If we assume 1 ppm = 1 mg solute/ 1 L solution

then in water
1 ppm = 1 mg solute / 1 Kg solution
1 ppm = 1 E-3 g solute / 1E3 g solution
1 ppm = (1 g solute / 1 g solution) * 1E-6

 

[shaboobly]

kg of solution and L of solution are not the same thing. you must take into account the mass of the solute when you are talking about kg of solution which would make the kg of solution greater than 1 kg because its water + the solute.

 

[milski]

This is exactly why I am confused. If we assume 1 ppm = 1 mg solute/ 1 L solution

then in water
1 ppm = 1 mg solute / 1 Kg solution
1 ppm = 1 E-3 g solute / 1E3 g solution
1 ppm = (1 g solute / 1 g solution) * 1E-6
1E+6 ppm = (1 g solute / 1 g solution)

You need the last line that I added. You are converting from mass ratio to ppm, not vice versa. That means you need to know how many ppm is 1 g/ 1 g, not the other way around.

 

[shaboobly]

You need the last line that I added. You are converting from mass ratio to ppm, not vice versa. That means you need to know how many ppm is 1 g/ 1 g, not the other way around.

your last line is equivalent. you still need to take into account the mass of the solute when talking about kg of solution because solution is solute+solvent

 

[milski]

your last line is equivalent. you still need to take into account the mass of the solute when talking about kg of solution because solution is solute+solvent

All the lines are equivalent. The question is why the conversion factor is 10^6 and not 10^-6.

 

[Testosterone]

Thanks for the help, but sorry I'm still not seeing how

1E+6 ppm = (1 g solute / 1 g solution)

is equivalent to

1ppm = (1g solute / 1 g solution ) * 10^6

 

[Testosterone]

kg of solution and L of solution are not the same thing. you must take into account the mass of the solute when you are talking about kg of solution which would make the kg of solution greater than 1 kg because its water + the solute.

I understand this, but adding 1 mg to 1 kg makes a very negligible difference to the total mass of the solution anyway.

 

[milski]

Thanks for the help, but sorry I'm still not seeing how

1E+6 ppm = (1 g solute / 1 g solution)

is equivalent to

1ppm = (1g solute / 1 g solution ) * 10^6

It is not - it is 10^-6 in the second equaiton. Look at what you initially wrote:

1 ppm = 1 gs/gs * 10^-6 (= 10^-6 gs/gs)

If you multiply both sides by 10^6, you get
10^6 ppm = 1 gs/gs.

In other words, for each 1 gs/gs you have 10^6 ppm.

 

[Testosterone]

It is not - it is 10^-6 in the second equaiton. Look at what you initially wrote:

1 ppm = 1 gs/gs * 10^-6 (= 10^-6 gs/gs)

If you multiply both sides by 10^6, you get
10^6 ppm = 1 gs/gs.

In other words, for each 1 gs/gs you have 10^6 ppm.

Ok yea exactly, so EK's definition is wrong then. Appreciate the help.

 

[milski]

Ok yea exactly, so EK's definition is wrong then. Appreciate the help.

I'm not sure how you got to the point that it is incorrect. All that they are telling you is that say 0.000001 gs/gs = 0.000001 gs/gs * 10^6 ppm /(gs/gs) = 1 ppm.

 

[Testosterone]

I'm not sure how you got to the point that it is incorrect. All that they are telling you is that say 0.000001 gs/gs = 0.000001 gs/gs * 10^6 ppm /(gs/gs) = 1 ppm.

😕Ok now I honestly can't tell if you are just trolling. You are both comfirming my doubts about EK's error and contradicting yourself at the same time. I agree completely with you that:

0.000001 gs/gs = 1 ppm *(I agree with you here)*

which equals

1E-6 gs/gs = 1 ppm

EK's formula was 1E6 (gs/gs) = 1 ppm, which is different from both yours and mines.

 

[milski]

I'm not trolling, not in the MCAT section at least.

EK's formula is:

ppm = (gs/gs) * 10^6, not 1 ppm = 10^6 (gs/gs). There is a significant difference between the two. A better and clearer way to write what EK is trying to say is ppm(mr) = mr * 10^6. You plug mass ratio and get ppm.

Let's try another way to look at it: if the mass ratio is 1, how many ppm is that?

M ppm = N (gs/gs) * 10^6 is yet another way to write it. If you know N, you get M by multiplying N by 10^6.

 

[Testosterone]

Eh, sorry it's not your fault at all, but I simply just can't wrap my head around the idea that ppm = (gs/gs) * 10^6 is significantly different from 1 ppm = (gs/gs) * 10^6.

It seems like wikipedia defines ppm as a dimensionless quantity (like mass ratio) times 10^-6. It doesn't even seem that popular of a notation in chemistry anyways. Either way I think ppm = 1 mg/kg would be a less confusing formula for the purposes of the MCAT, if it is even tested.

 

[milski]

The former is saying that N ppm = M (gs/gs) * 10^6, the latter is claiming that the above is correct for N=M=1. There is no implicit '1' in front of ppm in their formula - it is as many ppm as it turns out to be.

Either way, if you understand that say 0.001 g/1 g = 1000 ppm, you should be ok.

 

[V5RED]

Eh, sorry it's not your fault at all, but I simply just can't wrap my head around the idea that ppm = (gs/gs) * 10^6 is significantly different from 1 ppm = (gs/gs) * 10^6.

It seems like wikipedia defines ppm as a dimensionless quantity (like mass ratio) times 10^-6. It doesn't even seem that popular of a notation in chemistry anyways. Either way I think ppm = 1 mg/kg would be a less confusing formula for the purposes of the MCAT, if it is even tested.

Think about percents.

To determine mass percent we divide the mass of the solute by the mass of the solvent and then multiply by 100.

This gives us the percent which is the same as saying parts per hundred. If the mass of the solute is 1% of the solution mass, then for every 100 grams of solution, we have 1 gram of solvent.

Apply this to parts per million.

Another way to think about it is to think of these 3 percents. 0%, 50%, 100%

Obviously if solute is 0% of the solution then it is 0ppm
Obviously if solute is 50% of the solution then it is 500,000ppm
Obviously if solute is 100% of the solution then it is 1,000,000ppm

Does grams solute/grams solution*10^-6 get these obviously true results? No. In the case of the solution being 100% solute, the formula you have offered will tell you that there is 1 part solvent per million parts solution.

Does grams solute/grams solution*10^6 get these obviously true results? Yes. No. In the case of the solution being 100% solute, the formula EK has offered will tell you that there are 1 million parts solvent per million parts solution.

EK's formula is correct.

 

[Testosterone]

Thanks you guys. These make a ton more sense now. Essentially, a function ( F(x)= x * 10^6 ) and a function with a plugged in variable F(1) = (1* 10^-6) * 10^6 =1 are different.

 

[milski]

Thanks you guys. These make a ton more sense now. Essentially, a function ( F(x)= x * 10^6 ) and a function with a plugged in variable F(1) = (1* 10^-6) * 10^6 =1 are different.

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