Answer
a. $3.01 \times 10^{23} \space C \space atoms$
b. $7.71 \times 10^{23} \space C \space atoms$
c. $ 0.0867 \space mole \space of \space Fe$
d. $14.1 \space moles \space of \space C_2H_6O$
Work Step by Step
1. Conversion factors:
$$1 \space mole \space of \space X = 6.02 \times 10^{23} \space of \space X$$
a. $$0.500 \space mole\space of \space C \times \frac{6.02 \times 10^{23} \space C \space atoms}{1 \space mole \space of \space C} = 3.01 \times 10^{23} \space C \space atoms$$
b. $$1.28 \space mole\space of \space SO_2 \times \frac{6.02 \times 10^{23} \space SO_2 \space molecules}{1 \space mole \space of \space SO_2} = 7.71 \times 10^{23} \space C \space molecules$$
c. $$5.22 \times 10^{22} \space atoms \space of \space Fe \times \frac{1 \space mole \space of \space Fe}{6.02 \times 10^{23} \space Fe \space atoms} = 0.0867 \space mole \space of \space Fe$$
d. $$8.50 \times 10^{24} \space molecules \space of \space C_2H_6O \times \frac{1 \space mole \space of \space C_2H_6O}{6.02 \times 10^{23} \space C_2H_6O \space molecules} = 14.1 \space moles \space of \space C_2H_6O$$
