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

Answer:

1.67 × 10⁻⁷ mol H₂O

3.14 × 10¹³ atoms deuterium

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.

$3.00 \mu g \times \frac{1g}{10^{6}\mu g } \times \frac{1mol}{18.02g} = 1.67 \times 10^{-7} mol$

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.

$1.67 \times 10^{-7} molH_2O \times \frac{6.02 \times 10^{23}moleculesH_2O }{1molH_2O} \times \frac{2atomsH}{1moleculeH_2O} \times 0.0156 \% = 3.14 \times 10^{13} atomsD$