Question
How many atoms in total are present in $$1\,kg$$ of sugar ?
A.
$$7.92 \times {10^{25}}\,{\text{atoms}}$$
B.
$$6 \times {10^{23}}\,{\text{atoms}}$$
C.
$$6.023 \times {10^{25}}\,{\text{atoms}}$$
D.
$$1000\,{\text{atoms}}$$
Answer :
$$7.92 \times {10^{25}}\,{\text{atoms}}$$
Solution :
$${\text{One molecule of sugar}}$$ $$\left( {{C_{12}}{H_{22}}{O_{11}}} \right) = 45\,{\text{atoms}}$$
$$\eqalign{
& {\text{Number of moles of sugar}} \cr
& = \frac{{1000}}{{342}} \cr
& = 2.92 \cr
& {\text{Number of molecules}} \cr
& = 2.92 \times 6.023 \times {10^{23}} \cr
& = 17.60 \times {10^{23}}\,{\text{molecules}} \cr
& {\text{Number of atoms}} \cr
& = 45 \times 17.60 \times {10^{23}} \cr
& = 7.92 \times {10^{25}}\,{\text{atoms}} \cr} $$