[Rutherford]

Toothpaste “with fluorine” contains sodium fluorophosphate, Na₂PO₃F, and sodium fluoride. The total amount of fluorine of 0,100 % (of mass) of a certain toothpaste consists of 0,050 % (of mass) of each compound. Calculate the mass ratio of the two compounds.

The text looks ambiguous to me. Can someone interpret this part:

The total amount of fluorine of 0,100 % (of mass) of a certain toothpaste consists of 0,050 % (of mass) of each compound.

What is 0.100%?

[kriggy]

I would say that in 1000g of toothpaste you you have 1g of fluorine. From this 1g of fluorine 0,5g is bound in Na₂PO₃F and 0,5g in NaF

[Rutherford]

That seems logical.
In the question it is asked to calculate the mass ratio of the two compounds, but in the answer, percents were shown: 0.111 % of NaF and 0.379 % of Na₂PO₃F. I guess that these are mass percents and they correspond to the values I got now using your way. Still, I think that this part needs to be changed:

The total amount of fluorine...consists of 0,050 % (of mass) of each compound.

This would mean that 1g of fluorine consists of 0.0005g of fluorine from NaF and 0.0005g of fluorine from Na₂PO₃F. While it is irrational, it could be easily read that way (I don't see why it couldn't). If they gave 50% instead of 0.050% it would be much easier to understand, so now I think that they mistaken. Didn't they?

[Needaask]

Would it be like this: consider in 1000g so 1g of fluoride in total. And in Na₂PO₃F there is 0.5g of fluoride. So we can split that into Na+P+3O+F to find the number of moles of F and hence for the rest. So once we got their individual number of moles we can get its mass?

And by mass ratio don't they mean mass of Na2PO3F divided by mass of NaF?

[Rutherford]

That's how it should be, but in the text, I think they should have written 50% instead of 0.050%.

And by mass ratio don't they mean mass of Na2PO3F divided by mass of NaF?

Here is another mistake. In the answer, they didn't give the ratio, but the mass percents of these compounds in the paste, as I wrote in my previous post.

[Needaask]

That's how it should be, but in the text, I think they should have written 50% instead of 0.050%.

And by mass ratio don't they mean mass of Na2PO3F divided by mass of NaF?

Here is another mistake. In the answer, they didn't give the ratio, but the mass percents of these compounds in the paste, as I wrote in my previous post.

Hmm.. I understand the second mistake but I'm thinking that they meant 0.05% of the entire toothpaste? I don't think it really matters though because in the end the end you would still get a ratio.

But is my working sound to you? Like I treat 100% to be 1000g and then I get 0.05% of F and using the mole ratios I can find that that number is equal to the number of moles of Na2PO3F and from there I can just use moles=mass/Mr to get the mass of the whole compound?

[Rutherford]

Well, they said that the total mass of fluorine consists of 0.050% not the total mass of the whole paste. Your work is good, see if you can get the answer results: 0.111 % of NaF and 0.379 % of Na₂PO₃F.

[Big-Daddy]

The total percentage mass of fluorine in the toothpaste is 0.100%, but what on earth is that 0.050%? Does it mean half of the fluorine is bound in each? Or does it mean 0.050% of the fluorine is bound in each, and the remaining 99.90% is bound elsewhere?

[Big-Daddy]

I've got the answers, they do mean half of fluorine is bound in each for the answers to be 0.379% and 0.111%. You can use that with confidence.

If 0.050% of the fluorine was bound in each compound, we'd get 1.105·10^-4 as mass % for NaF and 3.79·10^-4 as mass % for Na₂PO₃F. (Actually that didn't need to be calculated out really - we've just shifted down 3 dp, just as the total % mass of F in toothpaste has been shifted down 3 dp.)

[Rutherford]

That's what I thought, but I wanted a second opinion. So it is 50%.

[Big-Daddy]

Yeah But the problem is still easy enough if it's 0.050% rather than 50%. Just note that n[Compound with F]=0.00050*n[F]/v[F in that Compound]. For both your compounds here v[F in that Compound]=1 so this reduces to n[Compound with F]=0.00050*n[F]. For the case the question actually means rather than says, it is n[Compound with F]=0.50*n[F]. With that it's quite simple to calculate, m[toothpaste] cancels out.

[Rutherford]

But it says:

The total amount of fluorine

The total amount should add to 100%, so if it were 0.05%, they would add just to 0.1% while in the text it is said total amount.

[Big-Daddy]

But it says:

The total amount of fluorine

The total amount should add to 100%, so if it were 0.05%, they would add just to 0.1% while in the text it is said total amount.

From what I have read, nothing in the problem precludes there from being other compounds including F in toothpaste, and you just have to work out the percentage mass of a certain two of them.

Regardless, it is clear from the solutions that 50% is what they meant.

[Corribus]

My interpretation was simple enough.  The toothpaste is 0.1% fluorine by weight, half of which comes from sodium fluorophosphate and half of which comes from sodium fluoride.  (That is 0.05% of the toothpaste by mass is fluorine from sodium fluorophosphates and 0.05% is fluorine from sodium fluoride.)

I don't really see how it could be interpreted any other way.  It seems pretty clear to me.

[Rutherford]

I see now  . They could have written:

consists of 0,050 % (of mass) of each compound (in respect to the mass of the whole paste).

to make it easier to understand, but now I see that it should be obvious even without it. Thanks for the correction.