Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

A sample of water contains x% of "D"_2"O". Its molecular weight is 19. The value of x is what?

50%

The idea here is that you need to use the fact that deuterium, "D", which is one of the three naturally occurring of hydrogen, "H", contains two nucleons in its nucleus.

color(white)()

As you know, the relative of an atom, A_r, is calculated by dividing the atomic mass of the atom, m_a, by 1/12"th" the mass of an atom of ""^12"C", which is equivalent to the mass of one nucleon, i.e. one proton or one neutron.

The relative atomic mass of hydrogen is approximately equal to 1 because its nucleus contains one proton. Since the nucleus of a deuterium atom contains a proton and a neutron, its relative atomic mass will be equal to 2.

Now, water, "H"_2"O", contains two hydrogen atoms and one oxygen atom. Heavy water, "D"_2"O", contains two deuterium atoms and one oxygen atom.

This means that the difference between the relative molecular mass of water and the relative molecular mass of heavy water will be equal to twice the difference between A_r of hydrogen and A_r of deuterium.

The relative atomic mass of oxygen is 16, which means that the relative molecular masses of water and of heavy water are

A_("r H"_2"O") = 2 xx 1 + 16 = 18

A_("r D"_2"O") = 2 xx 2 + 16 = 20

Your sample has an average relative molecular mass of 19, which can only mean that it contains equal amounts of water and of heavy water.

Mathematically, you can show this by using a system of two equations that have x as the decimal abundance of "H"_2"O" and y as the decimal abundance of "D"_2"O"

{(19 = x * 18 + y * 20), (color(white)(9)1 = x + y ) :}

This will get you

19 =18x + 20 - 20x

2x = 1 implies x = 1/2

This means that

y = 1 - 1/2 = 1/2

and thus your sample contains 50% "H"_2"O" and 50% "D"_2"O".