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I’m currently trying to learn some chemistry and have run into some trouble understanding some of the basics. The confusion stems from a passage in my textbook, so I will list the brief passage and then ask my question.

In addition to predicting molecular formulas, Avogadro’s hypothesis gives correct results for the relative atomic masses of the elements. Analysis by chemists during the 18th century had revealed that 1g of hydrogen combines fully with 8g of oxygen to make 9g of water. If Dalton’s formula for water, HO, were correct, then an atom of oxygen would have to weigh eight times as much as an atom of hydrogen; that is, Dalton’s assumption requires the relative atomic mass of oxygen to be 8 on a scale where the relative atomic mass of hydrogen is set at 1.

So far so good, I believe that oxygen has a relative mass of 8 because there are 8g of oxygen in the original reaction and likewise with the 1g of hydrogen, but this next part is where it starts to get confusing.

From Avogadro’s hypothesis, however, each water molecule contains twice as many atoms of hydrogen as oxygen, so to achieve the experimental mass relationship, each oxygen atom must have twice as large a relative atomic mass. This gives a relative atomic mass of 16 for oxygen, a result consistent with modern measurements.

Alright, so basically what I’m confused about is how they arrived at a relative atomic mass of 16 given that there is 8g of oxygen and 1g of H in the original experiment. What exactly are they observing in order to establish the relative atomic mass of oxygen as 16. Any help understanding this and relative mass in general would be greatly appreciated.

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It's because there's two hydrogen atoms in water, not one. In order to show you, let's assume we're making HO instead of H2O. This would clearly only require half the amount of hydrogen, but still the same amount of oxygen. Thus we have .5 grams of hydrogen combining with 8 grams of oxygen in a 1:1 relationship. Thus the oxygen weighs 16 times more than the hydrogen. Do you understand?

In H2O they combine in a 2:1 relationship. We have 1 gram of hydrogen combining with 8 grams of oxygen, but because there's 2 hydrogen for every oxygen, we actually need TWICE as many oxygen atoms to have the same amount of atoms. In other words, there will be the same number of atoms in 1g of hydrogen as there is in 16g of oxygen.

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This makes sense, thanks! –  Amateur Math Guy Feb 12 '13 at 13:52
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Basically, the error here is Dalton's in assuming that each mole of water contains an equal number of oxygen and hydrogen atoms. It doesn't; the molecular formula of water is H2O - each mole of water contains 2 moles of hydrogen (2*1g = 2g) and one mole of oxygen (16g). Water has a relative molecular mass of 18g. For every mole of oxygen there are two moles of hydrogen: $$\ce{2H2 + O2 -> 2H2O}$$

However, in this particular case, one mole of hydrogen (1g) and half a mole of oxygen (0.5*16 = 8g) are reacting to produce half a mole of water(9g). To get the original relative molar mass of oxygen they would have to double the mass of oxygen used - 8g - which would mean the result of 16g. This then gives a relative atomic mass of 16. Oxygen contains more isotopes (variants of an element with different relative atomic masses) than just oxygen-16 (such as oxygen-17 or oxygen-18), but to the level of accuracy we're working with it doesn't matter too much.

Basically, oxygen does have a relative atomic mass of 16. Ignoring isotopes, it could be worth looking at the (probably simplified) structure of the nuclei of oxygen and hydrogen . Certainly at this level, the relative mass of protons and neutrons is taken to be "1" (the two particles do have very slightly different masses, but this makes things easier). A 'typical' hydrogen nucleus just contains a proton with around 0 neutrons, so it has a relative atomic mass of 1 whereas a 'typical' oxygen nucleus contains 8 protons and around 8 neutrons; it has a relative atomic mass of 16.

However, as mentioned before, different isotopes containing different numbers of neutrons do exist. Relative atomic mass is just a weighted mean of these (which is why copper can have a relative atomic mass of 63.5 or chlorine can have one of 35.5), but the model above, whilst being a massive simplification and better for relative isotopic mass, might help you visualise the difference better.

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Why wouldn't it be $2H_{2} + O_{2} \rightarrow 2H_{2}O$ to get everything to balance? –  Amateur Math Guy Feb 12 '13 at 13:48
    
I made a mistake. Sorry, should have spotted that. Have now corrected it, so thanks for pointing that out. (actually, I'm kind of worried that this answer got upvoted, but it is the sort of mistake that is easy to miss) –  Alicia Butteriss Feb 12 '13 at 18:43
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