Solving Tritium Oxide in Ocean Water

[dajugganaut]

"Hot" Water

I have this problem in class that I could not solve. Could some one please help me?

I have 100mL of water made with tritium (radioactive isotope of hydrogen). If I were to pour this 100mL of hot water into the ocean (given the volume of the ocean is 1.3*(10^18)m^3) how many molcecules of the original 100mL of ditritium monoxide would be in a 100mL sample of the ocean water. Assume the tritium oxide has mixed thoroughly.

As this question deals with grams and molecules, I expect it to have something to do with avogadro's constant. Please suggest a few steps so that I can solve the problem. Thanks!

 

[chem_tr]

This is very easy man, just find that 100 mL of ditritium monoxide gives x moles, and this radioactive chemical is dissolved in a solvent, whose volume is $\displaystyle 1.3\times 10^{18}~m^3$. The cubic meters will cause you a trouble, but concentration can still be calculated from this; for example, it gives us the same result if we calculate millimoles over milliliters, moles over liters, or, just in our case, kilomoles over kiloliters (=one kiloliter is exactly one cubic meter, since one liter is one cubic decimeter).

I hope this makes sense.

 

[ravenprp]

Solving for the number of tritium oxide molecules in a 100mL sample of ocean water requires some basic understanding of chemistry and units. To solve this problem, we need to use the following steps:

1. Convert the given volume of ocean water (1.3*(10^18)m^3) to liters. This can be done by dividing the volume by 1000, since 1 m^3 is equal to 1000 liters. This will give us a volume of 1.3*(10^15) liters.

2. Convert the volume of 100mL of tritium oxide to liters by dividing it by 1000. This will give us a volume of 0.1 liters.

3. Use the molarity formula, M = moles/volume, to calculate the number of moles of tritium oxide in the 100mL sample. Since we are given the volume and the concentration (100mL and 1 mole/L, respectively), we can simply plug in these values to get the number of moles.

Moles of Tritium Oxide = (1 mole/L) x (0.1 L) = 0.1 moles

4. Now, we need to convert the number of moles to molecules using Avogadro's constant, which states that 1 mole of any substance contains 6.022 x 10^23 molecules. So, to get the number of molecules in 0.1 moles of tritium oxide, we multiply the number of moles by Avogadro's constant.

Number of Tritium Oxide molecules = (0.1 moles) x (6.022 x 10^23 molecules/mol) = 6.022 x 10^22 molecules

5. Finally, we need to calculate the number of molecules in a 100mL sample of ocean water. To do this, we divide the number of molecules in the 100mL sample of tritium oxide by the total volume of ocean water (1.3*(10^15) liters) and then multiply by the volume of the sample (100mL) to get the total number of molecules.

Number of Tritium Oxide molecules in 100mL of ocean water = (6.022 x 10^22 molecules) x (100mL/1.3*(10^15) liters) x (100m