Question

For isotopic analysis, an ice core sample was heated to produce gaseous H2O. If 3.00 μg of gaseous H2O was injected into a mass spectrometer:

How many moles of water were injected? Answer: 1.67×10−7
If the sample contains 0.0156% deuterium, how many deuterium atoms were injected?

Answer 1

1.67 × 10⁻⁷ mol H₂O

3.14 × 10¹³ atoms deuterium

Step-by-step explanation:

How many moles of water were injected?

We have 3.00 μg of gaseous H₂O. To calculate the number of moles of water we will use the following relationships:

• 1 g = 10⁶ μg
• The molar mass of water is 18.02 g/mol.

`3.00 \mu g * (1g)/(10^(6)\mu g ) * (1mol)/(18.02g) = 1.67 * 10^(-7) mol`

If the sample contains 0.0156% deuterium, how many deuterium atoms were injected?

We will use the following relationships:

1 mole of water contains 6.02 × 10²³ molecules of water.

There are 2 hydrogen atoms per water molecule.

0.0156% of hydrogen atoms are deuterium atoms.

`1.67 * 10^(-7) molH_2O * (6.02 * 10^(23)moleculesH_2O )/(1molH_2O) * (2atomsH)/(1moleculeH_2O) * 0.0156 \% = 3.14 * 10^(13) atomsD`