Measuring the Mass & Electric Charge of Molecules

[Const@ntine]

Homework Statement

Hi! So I stumbled upon this simple "plug n' play" exercise in my Physics textbook. Basically it gives you certain molecules/atoms, and tells you to measure the Electric Charge, and its Mass. Pretty simple, but I hit upon some hickups. Anyway, let's get to it:

Find the Electric Charge and Mass of the following (the answer must be written with 3 Significant Digits):

a) H⁺
b) Na⁺
c) Cl^-
d) Ca²⁺
e) N^3-
f) N⁴⁺
g) The nucleus of an atom N
h) H₂O^-

Homework Equations

Proton (p):
Mass: 1.67262*10^-27 kg
Electric Charge: +1.6021765*10^-19 C

Electron (e):
Mass: 9.1094*10^-26 kg
Electric Charge: -1.6021765*10^-19 C

Neutron (n):
Mass: 1.67493*10^-27 kg
Electric Charge: 0

The Attempt at a Solution

(a) H has 1 proton, and 1 electron. H⁺ is positively charged, a cation, so that means the sole electron has left. Therefore:

EC: +1.60*10^-19 C
Mass: 1.67*10^-27 kg

(b) And here's where I get stuck. Na has 11 protons and 11 electrons. Na⁺ is positively charged, meaning one electron has left, and so:

EC: +1.60*10^-19 C
Mass: 10*m_e + 11*m_p = 1.84*10^-26 kg

But the book's answer is 3.82*10^-26 kg. Am I missing something?

Any help is appreciated!

 

[mfb]

Sodium has neutrons.

 

[Const@ntine]

Sodium has neutrons.

I figured that was where the mistake was, but I can't find anywhere how many it has. The Periodic Table has only the Atomic Number, 11.

 

[Borek]

For light elements you can assume number of neutrons is identical to the number of protons.

I don't like the question though.

 

[Const@ntine]

For light elements you can assume number of neutrons is identical to the number of protons.

Oh, okay. I remembered from High School that we shouldn't assume that, since the number of neutrons and protons weren't usually equal, so I figured I either did something wrong in the computations, or there was some database with the numbers of neutrons as well as the protons, etc.

I don't like the question though.

Did I phrase the OP badly, or do you mean that it's a bad exercise? If it's the former, I tried to translate it as best as I could. If it's the latter, I guess because it leads people to making false assumptions between the corellation of neutrons and protons, right?

Continuing from Na, does the same hold true for the rest (p ~ n)?

 

[Borek]

Did I phrase the OP badly, or do you mean that it's a bad exercise? (...) If it's the latter, I guess because it leads people to making false assumptions between the corellation of neutrons and protons, right?

Not your fault, it is a problem with the question. Not only it forces you to assume equal number of protons and neutrons, but it also forces you to assume mass of an atom equals sum of masses of the particles it is made of. Both assumptions are false.

Continuing from Na, does the same hold true for the rest (p ~ n)?

Less and less, but yes, calcium is more or less the last element fro which p=n is close to the reality (note, that elements are mixtures of isotopes, which is another reason why assumption p=n is a poor one).

Chances are the problem is designed this way to make you aware of these things, but if so it should also ask you to compare your results with the data from the periodic table.

 

[Const@ntine]

Not your fault, it is a problem with the question. Not only it forces you to assume equal number of protons and neutrons, but it also forces you to assume mass of an atom equals sum of masses of the particles it is made of. Both assumptions are false.
Less and less, but yes, calcium is more or less the last element fro which p=n is close to the reality (note, that elements are mixtures of isotopes, which is another reason why assumption p=n is a poor one).

Chances are the problem is designed this way to make you aware of these things, but if so it should also ask you to compare your results with the data from the periodic table.

Ah, cotcha. It's the first problem of the chapter, so (intro to Electricity, Ch.1 of 12) so I pressume it's just there to give a general idea to the reader.

Thanks again for the help and the fast responses!

 

[epenguin]

Homework Equations

Proton (p):
Mass: 1.67262*10^-27 kg
Electric Charge: +1.6021765*10^-19 C

Electron (e):
Mass: 9.1094*10^-26 kg
Electric Charge: -1.6021765*10^-19 C

Neutron (n):
Mass: 1.67493*10^-27 kg
Electric Charge: 0

The Attempt at a Solution

(a) H has 1 proton, and 1 electron. H⁺ is positively charged, a cation, so that means the sole electron has left. Therefore:

EC: +1.60*10^-19 C
Mass: 1.67*10^-27 kg

I agree with Borek on the nature of this question, on the other hand it is making you turn up a few things.

I find what you say here slightly odd - there is nothing to take away, H⁺ just is the same thing as a proton.

(Although we sometimes write [H⁺] in solution chemistry when we don't really mean it, we mean something else, essentially [H⁺₃O])
Alerted by your talking of subtracting I wondered if you had actually subtracted the mass of the electron, in which case you would have got a wildly out result because - I assure you I don't remember these masses, perhaps I ought to - but I am very aware and so should you be that the mass of the electron is much much smaller than that of the proton so I at least could see you actually have it bigger! and I easily looked it up to be 9.10938356(11)×10^-31 g

 

[Const@ntine]

I agree with Borek on the nature of this question, on the other hand it is making you turn up a few things.

I find what you say here slightly odd - there is nothing to take away, H⁺ just is the same thing as a proton.

(Although we sometimes write [H⁺] in solution chemistry when we don't really mean it, we mean something else, essentially [H⁺₃O])
Alerted by your talking of subtracting I wondered if you had actually subtracted the mass of the electron, in which case you would have got a wildly out result because - I assure you I don't remember these masses, perhaps I ought to - but I am very aware and so should you be that the mass of the electron is much much smaller than that of the proton so I at least could see you actually have it bigger! and I easily looked it up to be 9.10938356(11)×10−³¹ g

Well, the book's question for (a) was "an ionized atom of Hydrogen, H⁺" so I assumed the electron had left. Either way, the book's answer for the Mass of H⁺ is supposed to be written in 3 Significant Digits, and it's given as 1.67*10^-27 kg, so it's possible he added both the proton and the electron (the result of m_e + m_p = 1.670911*10^-27 kg, so the same thing in 3 SD). What I'm curious about is whether or not does the Hydrogen have a neutron.

PS: I got those numbers for Part. 2 from my book.

 

[Borek]

But the book's answer is 3.82*10^-26 kg. Am I missing something?

Looks like even this result is incorrect, wolframalpha gives 3.68×10^-26.

 

[Const@ntine]

Looks like even this result is incorrect, wolframalpha gives 3.68×10^-26.

Yeah, Serway's books have such arithmetic errors in quite big ammounts. And to think that's the best of the Uni's Bibliography...

 

[Borek]

Note, that the number given in my previous post (despite being algebraically correct) has nothing to do with the real Na⁺ mass, which is substantially lower.

 

[Const@ntine]

Note, that the number given in my previous post (despite being algebraically correct) has nothing to do with the real Na⁺ mass, which is substantially lower.

I assume that's because the number of protons and neutrons isn't actually equal, as the book implies, correct?

 

[epenguin]

Well, the book's question for (a) was "an ionized atom of Hydrogen, H⁺" so I assumed the electron had left. Either way, the book's answer for the Mass of H⁺ is supposed to be written in 3 Significant Digits, and it's given as 1.67*10^-27 kg, so it's possible he added both the proton and the electron (the result of m_e + m_p = 1.670911*10^-27 kg, so the same thing in 3 SD). What I'm curious about is whether or not does the Hydrogen have a neutron.

PS: I got those numbers for Part. 2 from my book.

Yes the electron mass is less than 1000th of a proton's so I'm not expecting it to make any difference in the third-place whether it is there or not.
But anyway a hydrogen ion H⁺ is the same thing as a proton by itself. Hydrogen atom is a combination of a proton and an electron.
And no neutron.
However there do exist, quite minor in the world, other forms of hydrogen with a more complex nucleus. One is deuterium which as well as the proton has one neutron, and tritium which as well as the proton has two neutrons, and which is radioactive. These have a chemistry essentially the same as ordinary hydrogen, but being heavier the atom moves slower than ordinary hydrogen in chemical reactions. Which turns out to be useful property that can be exploited in investigating chemical mechanisms. (The radioactivity of tritium is also very useful).

When I said I don't remember these numbers, actually I do but not quite that way. I remember roughly the Avogadro number which is the number of atoms in a mole. This is one of the numbers always to be remembered. It then follows from the concept of mole that the mass of a hydrogen atom in grams (I still think in grams) is approximately the reciprocal of the Avogadro number.

We do on this homework help forum calibrate taking some account of known student background, e.g. of very young students, or those from disadvantaged places. However these are rather surprising questions and answers for someone describing himself as 'undergraduate'. Maybe your school studies had no physical science whatever? It could get you more appropriate help if you explain a sentence or two more of your background and present Study situation in your profile.

 

[Const@ntine]

Yes the electron mass is less than 1000th of a proton's so I'm not expecting it to make any difference in the third-place whether it is there or not.
But anyway a hydrogen ion H⁺ is the same thing as a proton by itself. Hydrogen atom is a combination of a proton and an electron.
And no neutron.
However there do exist, quite minor in the world, other forms of hydrogen with a more complex nucleus. One is deuterium which as well as the proton has one neutron, and tritium which as well as the proton has two neutrons, and which is radioactive. These have a chemistry essentially the same as ordinary hydrogen, but being heavier the atom moves slower then log me hydrogen in chemical reactions. Which turns out to be useful property that can be exploited in investigating chemical mechanisms. (The radioactivity is also very useful).

When I said I don't remember these numbers, actually I do but not quite that way. I remember the Avogadro number which is the number of atoms in a mole. This is one of the numbers always to be remembered. It then follows from the concept of mole that the mass of a hydrogen atom in grams (I still think in grams) is approximately the reciprocal of the Avogadro number.

Thanks for the general info!

We do on this homework help forum calibrate taking some account of known student background, e.g. of very young students, or those from disadvantaged places. However these are rather surprising questions and answers for someone describing himself as 'undergraduate'. Maybe your School studies had no physical science whatever? It coukd get you more appropriate help if you explain a sentence or two more of your background and present Study situation in your profile.

Well, Chemistry here was never about going in-depth. We did the classic stuff (Planck, Bohr, Schrödinger, Bonds), but never really "explored" the "fine-lines" or whatever. No Labs or any of that. That was back in High School.

Either way, I'm studying Physics, so this is just one of those "kinda Chemistry, kinda Physics" exercises at the start of the Chapter. It's really not a biggie, it's an ill-defined exercise that needed more info. I got where I was going wrong.

Thanks again for the help!

 

[Borek]

I assume that's because the number of protons and neutrons isn't actually equal, as the book implies, correct?

No, nuclei are lighter than the particles they are made of. Google for "mass defect".

 

[Borek]

However there do exist, quite minor in the world, other forms of hydrogen with a more complex nucleus. One is deuterium which as well as the proton has one neutron, and tritium which as well as the proton has two neutrons, and which is radioactive.

Up to ⁷H have been observed.

 

[mfb]

I assume that's because the number of protons and neutrons isn't actually equal, as the book implies, correct?

That is an issue as well. Hydrogen typically has no neutron (deuterium and tritium occur naturally, but they only make up a very small fraction of all hydrogen atoms).
For oxygen, nitrogen, sodium and calcium, the assumption of equal numbers of protons and neutrons are reasonable, these isotopes are the most common ones. You don't have to make that assumption, however, you can look up which isotopes exist and how common they are.
For chlorine, that approach doesn't work any more. It has 17 protons, and chlorine nuclei with 17 neutrons decay within seconds. There are actually two stable isotopes, with 18 and 20 neutrons, respectively. The first one makes up 75% and the second one makes up 25% of the natural chlorine composition, clearly both are relevant. So which one are you supposed to take? Or does the problem ask you to calculate the average?