## Homework E19

DTingey_1C
Posts: 55
Joined: Fri Aug 30, 2019 12:16 am

### Homework E19

Here is the problem E19 from the textbook:

A report stated that the Sudbury Neutrino Observatory in Sudbury, Canada, uses 1.00×10^3 tonne (1t=10^3kg)of heavy water, D2O, in a spherical tank of diameter 12 m to detect neutrinos. The density of normal water (H2O) at the temperature of the tank is 1.00g⋅mol^−3
(a) Using a molar mass for deuterium of 2.014g⋅mol^−1, calculate the molar mass of D2O
(b) Assuming that the volume occupied by a D2O molecule is the same as that occupied by an H2O molecule, calculate the density of heavy water.
(c) Calculate the volume of the tank in cubic meters from your density data and the given mass of the heavy water, then compare this volume with the volume of the tank calculated from its reported diameter.
(d) Is the reported mass of heavy water accurate? (e) Is the assumption you made in part (b) reasonable? Explain your reasoning. (The volume of a sphere of radius r is V=4/3πr3)

I understand how to get the molar mass in A, but how do you find the density of the D20 molecule when it doesn't give you the volume of an H20 molecule. Thanks.

Lelija Kazlauskas 3J
Posts: 50
Joined: Thu Jul 11, 2019 12:16 am

### Re: Homework E19

To find the density of a single water molecule, you have to use Avogadro's constant.

There are 6.022x10^23 molecules of H2O in 18.0158 g of water.

Then you divide that molar mass (18.0158 g) by Avogadro's constant to get the mass of one water molecule (~ 2.99×10^-23 g).

The density of water is 1 g/mL.

Thus, the volume of one water molecule is the mass of one water molecule, divided by the density of water.

The volume of water you get is 2.99×10^-23 mL.

Then you can use the molar mass of the heavy water, divided by this volume to get your answer.