Question

4.) there are ____ moles in 9.01 x 10^23 molecules of water. (1 point)
o 1.50
o 15.0
o 0.150
o none of the above
5.) a given sample of caffeine, c8h10n4o2, has 6.47 x 10^22 atoms of carbon. how many atoms of hydrogen in the same sample? (1 point)
o 5.18 x 10^22 h atoms
o 8.09 x 10^22 h atoms
o 6.47 x 10^22 h atoms
o 6.47 x 10^23 h atoms

Explanation:

Step1: Recall Avogadro's number

Avogadro's number $N_A = 6.022\times 10^{23}\text{ molecules/mol}$.

Step2: Calculate moles of water

Use the formula $n=\frac{N}{N_A}$, where $N = 9.01\times 10^{23}$ molecules. So $n=\frac{9.01\times 10^{23}}{6.022\times 10^{23}} = 1.50$ mol.

Step1: Determine ratio of C to H in caffeine

In $C_8H_{10}N_4O_2$, the ratio of carbon to hydrogen atoms is $C:H=8:10 = 4:5$.

Step2: Calculate number of hydrogen atoms

Let $N_H$ be the number of hydrogen atoms and $N_C=6.47\times 10^{22}$ be the number of carbon atoms. Since $\frac{N_H}{N_C}=\frac{5}{4}$, then $N_H=\frac{5}{4}\times N_C=\frac{5}{4}\times6.47\times 10^{22}= 8.09\times 10^{22}$ atoms.

Answer:

A. 1.50