To determine the mass of nickel in a 2,400 gram sample of propanol where the concentration of nickel is 20 ppb (parts per billion), let us break down the steps:
1. Understand the concentration in ppb:
- ppm (parts per million) means 1 unit of substance per 1,000,000 units of the medium.
- Similarly, ppb (parts per billion) means 1 unit of substance per 1,000,000,000 units of the medium.
2. Convert the concentration from ppb to a fractional form:
- 20 ppb can be represented as [tex]\( \frac{20}{1,000,000,000} \)[/tex].
3. Calculate the mass of nickel:
- We know the sample mass is 2,400 grams.
- Therefore, the mass of nickel in the sample is calculated by multiplying the sample mass by the concentration fraction:
[tex]\[
\text{Mass of Nickel} = \text{Sample Mass} \times \frac{\text{Concentration (ppb)}}{1,000,000,000}
\][/tex]
4. Perform the multiplication:
- [tex]\(\text{Mass of Nickel} = 2,400 \, \text{g} \times \frac{20}{1,000,000,000}\)[/tex]
[tex]\[
\text{Mass of Nickel} = 2,400 \times 20 \times 10^{-9} \, \text{g}
\][/tex]
[tex]\[
\text{Mass of Nickel} = 48,000 \times 10^{-9} \, \text{g}
\][/tex]
5. Simplified result:
- Simplify [tex]\(48,000\)[/tex] times [tex]\(10^{-9}\)[/tex]:
[tex]\[
48,000 \times 10^{-9} = 4.8 \times 10^{-5} \, \text{g}
\][/tex]
Thus, the mass of nickel in the 2,400 gram sample of propanol is [tex]\(4.8 \times 10^{-5} \, \text{g}\)[/tex].
Comparing this result to the given options:
A. [tex]\(0.0083 \, \text{g Ni}\)[/tex]
B. [tex]\(4.8 \times 10^3 \, \text{g Ni}\)[/tex]
C. [tex]\(8.3 \times 10^0 \, \text{g Ni}\)[/tex]
D. [tex]\(0.048 \, \text{g Ni}\)[/tex]
None of these options exactly match our calculated result. Therefore, the question or answer choices might contain an error and should be reviewed for possible correction.
