Question

The concentration of titanium in the South Pacific Ocean, near the island nation of Fiji, has been found to be approximately \(3.0 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}\). Calculate the concentration in ppm, ppb, or ppt as appropriate,

Short answer

The concentration is approximately 0.14361 ppb.

Step-by-step solution

Understanding Units

When dealing with concentrations such as ppm (parts per million), ppb (parts per billion), or ppt (parts per trillion), it's essential to understand what each unit represents. Ppm is \(10^{-6}\), ppb is \(10^{-9}\), and ppt is \(10^{-12}\) in terms of the total amount.

Determine Appropriate Unit

Given \(3.0 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}\), we need to convert this molar concentration into a suitable unit. Since the concentration is given as \(10^{-9}\), the most appropriate unit for expression is ppb (parts per billion).

Calculate Molar Mass of Titanium

Titanium (Ti) has an atomic weight of approximately \(47.87\, ext{g/mol}\). We need this value to convert the molar concentration to mass concentration.

Convert Molar Concentration to Mass Concentration

Multiply the molar concentration by the molar mass of titanium to convert \(3.0 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}\) to \(3.0 \times 10^{-9} \times 47.87\, ext{g/L} = 1.4361 \times 10^{-7} \mathrm{~g} \mathrm{~L}^{-1}\).

Express Concentration in ppb

Since the concentration is \(1.4361 \times 10^{-7} \mathrm{~g} \mathrm{~L}^{-1}\), when we express it in ppb, we multiply by 1000 to convert g/L to µg/L, obtaining \(1.4361 \times 10^{-4} \mathrm{~µg}/\mathrm{~L}\) or approximately 0.14361 \(\mathrm{~ppb}\).

Key concepts

Molar Concentration

Molar concentration is a way to express the amount of a substance in a solution. It is defined as the number of moles of solute per liter of solution. This unit is commonly referred to as molarity and is denoted in units of moles per liter (mol/L or M).

For example, in the given exercise, the molar concentration of titanium is provided as \(3.0 \times 10^{-9} \, \mathrm{mol/L}\). This means that for every liter of ocean water, there are approximately \(3.0 \times 10^{-9}\) moles of titanium present.

Understanding molarity is crucial because it allows chemists to calculate how much of a substance is present in a solution, which is essential for reactions and other chemical processes.

Atomic Mass

Atomic mass, sometimes referred to as atomic weight, is the average mass of an atom of an element, measured in atomic mass units (amu). It is based on the weighted average of all the isotopes of an element that occur naturally.

The atomic mass helps us convert between different units of concentration. In the exercise, we are given that the atomic mass of titanium (Ti) is approximately 47.87 g/mol. This value allows us to turn a molar concentration, in this case around \(3.0 \times 10^{-9} \, \mathrm{mol/L}\), into a mass concentration measured in grams per liter (g/L).

The concept of atomic mass is fundamental as it helps you relate molar quantities to measurable masses in laboratory settings.

Parts Per Billion

Parts per billion (ppb) is a unit of concentration that expresses the amount of a solute in a billion parts of solution, making it suitable for very dilute concentrations. For instance, 1 ppb indicates one part of a solute per one billion parts of solution.

In the given exercise, after calculating, we find the titanium concentration in ppb as approximately 0.14361 ppb. This is particularly useful in environmental studies where even trace amounts of substances can have significant impacts.

PPB is often preferred over molar concentration in cases where the solute concentration is extremely low, as it provides a more intuitive sense of the amount present.

Unit Conversion

Unit conversion involves changing a measurement to a different unit, while retaining the same value. In chemistry, unit conversions are crucial, especially when dealing with various units of concentration like mol/L, g/L, and ppb.

To solve the exercise, the molar concentration of titanium needed to be converted from mol/L to g/L, and then to µg/L, and finally to ppb. The steps involved multiplying the molar concentration by the atomic mass to obtain g/L. Then, converting g/L to µg/L simplifies expressing the concentration in ppb.

Unit conversion is a versatile tool in any chemist's toolkit. It allows scientists to interpret data in the units most appropriate for their particular context, making results more relevant and understandable.