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 * 10^3 gal of seawater.

Verified step by step guidance

Convert the volume of seawater from gallons to liters using the conversion factor: 1 gallon = 3.78541 liters.

Calculate the mass of seawater in kilograms, assuming the density of seawater is approximately 1.025 kg/L.

Determine the mass of gold in the seawater using the concentration of 13 ppt (parts per trillion), which means 13 grams of gold per 10^12 grams of seawater.

Use the mass of seawater calculated in step 2 to find the mass of gold by setting up a proportion based on the ppt concentration.

Convert the mass of gold from grams to the desired unit if necessary, ensuring the final answer is in grams.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concentration Units

Concentration is a measure of the amount of a substance in a given volume of solution. In this case, parts per trillion (ppt) indicates the number of parts of gold per trillion parts of seawater. Understanding how to convert between different concentration units is essential for calculating the total amount of gold in a specified volume of seawater.

Volume Conversion

To solve the problem, it is necessary to convert the volume of seawater from gallons to a metric unit, such as liters or milliliters, since concentration is often expressed in grams per liter. Knowing the conversion factors between gallons and liters (1 gallon = 3.78541 liters) is crucial for accurate calculations.

Mass Calculation

Once the concentration of gold in seawater and the total volume of seawater are known, the mass of gold can be calculated using the formula: mass = concentration × volume. This step involves multiplying the concentration of gold (in grams per liter) by the total volume of seawater (in liters) to find the total mass of gold present.

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