Relative abundance of H-2 (deuterium) is 0.015% and O-18 is 0.20%. Calculate the number of D2O18 molecules in a 1mol of natural water sample?
1 mol H2O has a mass of 18.015 grams and you can get this number by adding 2*atomic mass H + 1*atomic mass O.
In that 18.015 g there will be 6.022E23 molecules of water in one of several forms. What kind of forms? If we call 1H p for protium, 2H D for deuterium, and O16 and O18, we can get the following forms of water.
P2O16
PDO16
P2O18
PDO18
D2O16
D2O18
If I didn't miss anything that is 6 different ways of putting p and D and O16 and O18 together.
How many grams D do we have in 18.015 g H2O. That's 18.015 x 0.00015 = about 0.0027 grams D or 0.0027/2.014 = about 0.00134 mols D.
Do the same for O18 and we get
18.015 x 0.002 = 0.036 or 0.036/18 = 0.002 mols O18.
# atoms D = 0.00134*6.02E23=about 8.07E20
# atoms O18 = 0.002*6.02E23 = about 12*10^20. With a ratio of 2:1 H:O, there aren't enough H atoms to use all of the O18. Therefore, if we use all of the D atoms to form those shown above,
1/6 of those D atoms will go to form D2O18 so 1/6*8E20 = about 1.3 E20 D2O18. There will be approximately the same number of D2O16, HDO16, and HDO18 give or take a few. I don't think that uses up all of the O18 out there so there may be a few trillion of those flying around looking to form P2O18. You might want to look over this critically; as you can see I've made some assumption and some guesses.
To calculate the number of D2O18 molecules in 1 mole of natural water sample, you need to consider the relative abundance of deuterium (H-2) and oxygen-18 (O-18).
Step 1: Calculate the number of moles of deuterium (H-2):
- Relative abundance of H-2 = 0.015%
- 0.015% can be written as 0.00015 (decimal form)
- Multiply 0.00015 by 1 mole (the total number of molecules in 1 mole)
- The result gives you the number of moles of H-2 in 1 mole of water sample.
Step 2: Calculate the number of moles of oxygen-18 (O-18):
- Relative abundance of O-18 = 0.20%
- 0.20% can be written as 0.002 (decimal form)
- Multiply 0.002 by 1 mole (the total number of molecules in 1 mole)
- The result gives you the number of moles of O-18 in 1 mole of water sample.
Step 3: Calculate the number of D2O18 molecules:
- Since there are 2 deuterium atoms (H-2) and 1 oxygen-18 (O-18) atom in each D2O18 molecule, you need to multiply the number of moles of H-2 by 2 and the number of moles of O-18 to find the number of moles of D2O18 molecules.
- Then, multiply this quantity by Avogadro's number (6.022 x 10^23 molecules/mol) to find the actual number of D2O18 molecules in 1 mole of water sample.
By following these steps and performing the calculations, you will get the number of D2O18 molecules in 1 mole of natural water sample.