To determine the mass of a sample of sodium bicarbonate in nanograms (ng) when given the mass in kilograms (kg), we will follow these steps:
1. Conversion from kilograms to grams:
- We know that [tex]\(1 \, \text{kg}\)[/tex] is equal to [tex]\(1,000 \, \text{grams}\)[/tex] (g).
- Therefore, to convert the given mass of 2.1 kilograms to grams, we multiply the mass in kilograms by 1,000.
[tex]\[
2.1 \, \text{kg} \times 1,000 \, \text{g/kg} = 2,100 \, \text{g}
\][/tex]
2. Conversion from grams to nanograms:
- We also know that [tex]\(1 \, \text{gram}\)[/tex] is equal to [tex]\(1 \times 10^9 \, \text{nanograms}\)[/tex] (ng).
- To convert the mass from grams to nanograms, we multiply the mass in grams by [tex]\(1 \times 10^9\)[/tex].
[tex]\[
2,100 \, \text{g} \times 1 \times 10^9 \, \text{ng/g} = 2.1 \times 10^{12} \, \text{ng}
\][/tex]
Combining these conversions, we find that the mass of the sodium bicarbonate sample in nanograms is given by:
[tex]\[
2.1 \, \text{kg} = 2.1 \times 10^{12} \, \text{ng}
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{2.1 \times 10^{12} \, \text{ng}}
\][/tex]
