Problem 96 - Chemistry The Central Science In Si Units

Question

The concentration of gold in seawater has been reported to be between 5 ppt (parts per trillion) and 50 ppt. Assuming that seawater contains 13 ppt of gold, calculate the number of grams of gold contained in \(1.0 \times 10^{3}\) gal of seawater.

Step-by-Step Solution

Answer

The seawater contains approximately \(4.92 \times 10^{-8}\) grams of gold.

Step 1: Convert Gallons to Liters

First, convert the volume of seawater from gallons to liters. Use the conversion factor: 1 gallon = 3.78541 liters. Multiply the number of gallons by this conversion factor: \\(1.0 \times 10^3 \text{ gal} \times 3.78541 \frac{\text{L}}{\text{gal}} = 3785.41 \text{ L}\).

Step 2: Determine Concentration in Weight

Convert the gold concentration from parts per trillion (ppt) to grams per liter (g/L). Given 13 ppt means 13 grams of gold per \(10^{12}\) grams of seawater, we find: \\(13 \text{ ppt} = 13 \times 10^{-12} \text{ g/L}\).

Step 3: Calculate Total Gold Mass

Now calculate the total mass of gold in the given volume of seawater. Multiply the volume in liters by the concentration in grams per liter: \\(3785.41 \text{ L} \times 13 \times 10^{-12} \frac{\text{g}}{\text{L}} = 4.921033 \times 10^{-8} \text{ g}\).

Key Concepts

Unit Conversion

Unit conversion is a crucial step in calculations like our seawater example. When we have measures given in one unit and need them in another, we rely on conversion factors. In our exercise, we need to know how much seawater we have in liters, but it's originally given in gallons. Since 1 gallon equals 3.78541 liters, converting is simple. Multiply the number of gallons by 3.78541 to get the volume in liters.
So, for 1000 gallons of seawater, the conversion goes like this:

• 1000 gal
• Multiplied by 3.78541 L/gal.
• Results in 3785.41 liters.

This unit conversion allows us to proceed with our calculations using SI units, which makes further chemical computations more straightforward.

Parts Per Trillion

Parts per trillion (ppt) is a unit of measurement used to describe very small concentrations. It's used for parts of a substance per trillion parts of the total mixture. This is a common unit in chemistry for substances present in tiny amounts, like gold in seawater. - 1 ppt means there is 1 gram of a substance in 1 trillion grams (or liters, since we assume density similar to water) - In this case, 13 ppt of gold tells us there are 13 grams of gold per 10¹² grams of seawater For ease of calculation, we often convert ppt into grams per liter (g/L) because it's more direct for use in mass calculations when dealing with large volumes, like in our example. Simply, 13 ppt becomes 13 x 10^-12 g/L.

Mass Calculation

In mass calculations for chemical concentration problems, once you've converted your units correctly and understood the concentration, you can calculate the mass of a specific substance present in a mixture. Our exercise requires us to calculate the total mass of gold. With the volume in liters and the concentration in g/L, the calculation becomes straightforward multiplication. First, you take the volume of the seawater, which is 3785.41 liters from our conversion step. Then use the concentration, which we earlier found to be 13 x 10^-12 g/L for gold. To get the total mass:

• Multiply 3785.41 L by 13 x 10^-12 g/L.
• The result is 4.921033 x 10^-8 grams.

This tiny number illustrates how little gold is present in such a large volume of seawater, confirming the very dilute concentration we expressed in ppt.

Chemical Concentration

Chemical concentration refers to how much of one substance is present in a defined volume of a solution or mixture. It's expressed in various units like molarity, or as shown in our problem, parts per trillion (ppt). Understanding concentrations is key for chemists to determine the abundance of a substance and make various applications, such as extraction and resource estimation. In seawater, the concentration of elements like gold is minute, hence the use of ppt to express its value. This informs us about potential costs and feasibility for extraction. Gold's concentration in seawater reflects its rarely detectable abundance, and answers why mining in the ocean may not be viable despite our calculations showing how much gold could be present in large volumes.