Let's break down the problem step-by-step to find out how much mass of lead is present in the solution.
1. Understand the given values:
- Lead concentration: 400 ppb (parts per billion)
- Volume of solution: 10 kL (kiloLiters)
- Density of the solution: 1000 g/L (grams per Liter)
2. Convert the volume from kiloLiters to Liters:
Since 1 kiloLiter (kL) is equal to 1000 Liters (L), we multiply the volume by 1000:
[tex]\[
\text{Volume in Liters} = 10 \, \text{kL} \times 1000 \, \frac{\text{L}}{\text{kL}} = 10000 \, \text{L}
\][/tex]
3. Calculate the mass of the entire solution in grams:
The mass of the solution can be found by multiplying the volume in Liters by the density (given in grams per Liter):
[tex]\[
\text{Mass of solution} = \text{Volume} \times \text{Density} = 10000 \, \text{L} \times 1000 \, \frac{\text{g}}{\text{L}} = 10000000 \, \text{g}
\][/tex]
4. Calculate the mass of lead in the solution:
The concentration is given in parts per billion (ppb), which means 400 parts of lead per 1 billion parts of the solution. To find the mass of lead, we can use the following proportion:
[tex]\[
\text{Mass of lead} = \left( \frac{\text{Concentration}}{10^9} \right) \times \text{Mass of solution} = \left( \frac{400}{10^9} \right) \times 10000000 \, \text{g}
\][/tex]
5. Simplify the calculation:
[tex]\[
\text{Mass of lead} = \left( \frac{400}{1000000000} \right) \times 10000000 \, \text{g} = 4 \, \text{g}
\][/tex]
So, the mass of lead in 10 kL of this solution is [tex]\( 4.0 \)[/tex] grams.
