Chapter 2 · Terminology, Standards, and Mass Spectrometry

Problem 1

1. A sample of sphalerite (ZnS) has a δ³⁴S value of 12.39‰ (the raw value) relative to the working standard of the laboratory. This working standard has a δ³⁴S value of −4.66‰ relative to CDT. What is the δ³⁴S value of the sphalerite relative to CDT?
2. Graphitized diamond from Beni Bousera has a δ¹³C value of −4.22‰ relative to the working standard. The δ¹³C value of the working standard in the laboratory is −22.68‰ relative to VPDB. What is the δ¹³C value of the graphitized diamond relative to VPDB? reconstructed [Assignment of the two printed values to sample and standard was reconstructed; the result (≈−26.8‰) is consistent with published Beni Bousera graphite values.]

Problem 2

The working standard CO₂ used on a certain mass spectrometer has a δ¹⁸O value of 38.72 per mil relative to VSMOW. If a sample of CO₂ has a δ¹⁸O value of −14.57 per mil relative to this working standard,

1. What is its value relative to VSMOW?
2. What is its value relative to VPDB?

Worksheet (Problems 1 and 2)

[Worksheet constructed. Each row is one conversion with equation (2.3); in row 4, first convert the working standard to the VPDB scale in C4 using the KA and KB constants.]

Related interactive plots: delta algebra, scale conversions.

Problem 3

A ³²S/³⁴S ratio of 21.56 was reported for a sample of seawater sulfate in the early days of stable isotope geochemistry, when sulfur isotope compositions were reported as absolute ratios. Given that the absolute sulfur isotope ratio of Cañón Diablo Troilite (CDT) is 22.22, what is δ³⁴S (CDT) of this sulfate sample?

[Worksheet constructed.]

Problem 4

There was a computer crash after an important nitrogen sample was analyzed on the mass spectrometer. No information was saved, other than the voltages of the masses 28 and 29 (N₂) for the sample and the standard. (See the table in the worksheet.) Assuming that the reference gas has a δ¹⁵N value of −0.57‰ relative to AIR, what is the δ¹⁵N value of the sample relative to AIR?

[Worksheet constructed; voltages as printed.]

Problem 5

Vapor in oxygen isotope equilibrium with liquid water at 10 °C has a δ¹⁸O value of −13.42‰. What is the δ¹⁸O value of the water? α¹⁸O(l–v) = 1.0101 at 10 °C.

Problem 6

Quartz from the silica–carbonate rock in Trench 14 at the proposed disposal site for nuclear waste at Yucca Mountain, Nevada, has a δ¹⁸O value of 24.4‰. Given that

1. What would be the temperature of formation of this quartz if it formed in isotopic equilibrium with local groundwater whose δ¹⁸O = −11.6‰?
2. What temperature would be obtained if you merely subtracted δ values instead of using the 10³lnα value?
3. What would the δ¹⁸O value of water in equilibrium with this quartz need to be in order for the temperature of formation to be 300 °C?

[Worksheet constructed.]

Related interactive plot: 1/T² thermometer.

Problem 7

The term ε is commonly defined for phases a and b as ε_a–b = 1000(α_a–b − 1). For δ_b = δ_a − 10, show that the equality ε_a–b = δ_a − δ_b is valid when δ is close to zero, but invalid if δ is very different from 0 (e.g., 100‰).

[Worksheet constructed.]

Problem 8

Correct the following sentences:

1. Snow falling in the Sierra Nevada mountains is isotopically depleted. Del values of snow from this region have compositions of about −116.
2. The carbon signature of the Hawaiian nodule was −2 per mil, a value which is heavier than most mantle rocks.
3. Sulfur in these samples was analyzed and found to have no relation to the signature of carbon.

Problem 9

Write an expression for the sulfur isotope exchange reaction between pyrite and sphalerite.

Problem 10

Derive equation (2.3), δ_X–B = δ_X–A + δ_A–B + 0.001·δ_X–A·δ_A–B, using the definitions of α and δ.

Problem 11

Give three isotopologues of water with the same mass.

Problem 12

In this chapter, it is stated that “A sample with a δ¹⁸O value of +19.7‰ has an ¹⁸O/¹⁶O ratio that is 19.7 per mil, or 1.97 percent, higher than that of the standard.” If the standard VSMOW has an ¹⁸O/¹⁶O ratio of 2005.20·10⁻⁶, calculate the ¹⁸O/¹⁶O ratio of the sample, using the stated expression. Show that you get the same answer as when you use the definition of delta, given in equation (2.1).

[Worksheet constructed.]

Problem 13

The Merriam–Webster dictionary gives the following definition of an isotope: “any of two or more species of atoms of a chemical element with the same atomic number and nearly identical chemical behavior but with differing atomic mass or mass number and different physical properties”. What is wrong with this definition? How could you improve on it?

Problem 14

For a laboratory experiment, you wish to make a liter of water with a δD value of +500‰, starting with a mixture of normal water (δD = −90‰) and pure D₂O. How much D₂O must you add to 1 liter of water?

[Worksheet constructed; the mole and density constants for the volume conversion are supplied as parameter cells and are not printed in the problem.]