Are parts per million (ppm) by number of moles and volume...

Are parts per million (ppm) by number of moles and volume the same for a gas? The mixing ratio is sometimes used in atmospheric science and it is defined as the number of moles of a substance to the number of moles of everything else (not including the given substance). Sometimes the mixing ratio is similarly defined by mass rather than moles so some care should be taken to determine the definition. At what concentration limit will ppm and mixing ratio be equivalent?

Key Concepts

Mixing Ratio

The mixing ratio is a dimensionless quantity that compares the amount of a particular component (by moles or mass) to the amount of all other components in a mixture. In atmospheric sciences, it is often used to quantify trace gases by expressing the ratio of the number of moles of that gas relative to the number of moles in the rest of the air.

Parts Per Million (ppm)

Parts per million (ppm) is a unit of concentration that denotes one part of a constituent per one million parts of the mixture. When expressed by number, it typically implies a mole fraction of 10??, and when expressed by volume it represents a similar ratio for gaseous mixtures under ideal conditions.

Dilute (Trace) Limit Equivalence

The equivalence between ppm and the mixing ratio occurs under the dilute limit, where the concentration of the trace component is extremely low relative to the total composition of the mixture. In this limit, the differences that may arise from using number or volume basis become negligible, making ppm directly comparable to the mixing ratio.

Transcript

00:02 Hi there.

00:03 In this question, we are converting from parts per million or parts per billion, depending on the problem, to molarity.

00:12 So it is important to know that ppm or parts per million for a dilute solution would be the same as one milligram of solute for every liter of solution.

00:40 Similarly, parts per billion, but now we are talking about billion instead of million, so that's another factor of 10 to the third, this would be equal to one microgram of the solute for every leader of solution.

01:08 So using this information should allow us to go ahead and convert from parts per million or parts per billion to molarity.

01:17 Remember, of course, molarity, is moles of solute per liter of solution.

01:33 All right, with all of that information in mind, let's go ahead and get started.

01:37 Letter a gives us 5 .0 parts per billion.

01:46 So based upon what we have up here for parts per billion, this 5 .0 parts per billion would be the same as 5 .0 micrograms of the solute and the solute in this case is hg per liter of solution.

02:16 All right.

02:18 So that gives us a good starting point because we know molarity is moles per liter.

02:23 So if we can convert the micrograms of mercury to moles, we will have molarity.

02:30 So let's go ahead and do that.

02:31 First thing i want to do is to convert to grams.

02:35 So there are one times 10 to the 6 micrograms.

02:41 Of mercury in every gram of mercury.

02:45 I wanted to convert to grams so that now i can use molar mass.

02:50 Looking at the periodic table, there's 200 .6 grams of mercury in every mole of mercury.

03:05 Right.

03:05 If we check out what units have canceled, micrograms have canceled, grams have canceled, we are left with moles per liter.

03:14 And those are the exact units.

03:18 That we need for molarity.

03:21 So i'm going to grab my calculator now and calculate the answer, rounding it to two significant figures because that's what we were given in the problem.

03:30 I get 2 .5 times 10 to the negative 8 moles per liter or molar.

03:38 All right, so that is the general format we are going to follow for each of these problems.

03:42 Let's move on to letter b.

03:45 In letter b, we have 1 .0 parts per billion of chcl3.

03:54 Again, this is parts per billion, so that would be 1 .0 micrograms of chcl3 in every liter of solution.

04:11 Changing micrograms to grams, 1 times 10 to the 6 micrograms in every gram of chcl3.

04:21 Then i need the molar mass of chcl3, looking at the periodic table, adding together one carbon, one hydrogen, and three chlorines gives me 11 .37 grams of chcl3 in every mole.

04:44 Just like in the previous problem, all of my units will cancel except for moles per liter, which is molarity.

04:52 Calculating the answer, i get 8 .4 times 10 to the negative ninth molar.

05:00 So these are very dilute solutions, as you might have guessed, when you're talking in terms of one part per billion.

05:09 Let's go on to part c.

05:10 Part c, we are bumping it up to parts per million...

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