use the periodic table to determine how many atoms of phosphorus (p) are in a sample that has a mass of…

Answer:

C. $3.36\times 10^{24}$ atoms

Explanation:

Step1: Find molar - mass of phosphorus

From the periodic table, the molar mass of phosphorus ($P$) is $M = 30.97\ g/mol$.

Step2: Calculate the number of moles

The number of moles ($n$) is calculated using the formula $n=\frac{m}{M}$, where $m = 172.90\ g$ and $M = 30.97\ g/mol$. So, $n=\frac{172.90\ g}{30.97\ g/mol}\approx5.58\ mol$.

Step3: Use Avogadro's number

Avogadro's number $N_A=6.022\times 10^{23}\ atoms/mol$. The number of atoms ($N$) is given by $N = n\times N_A$. Substituting $n = 5.58\ mol$ and $N_A=6.022\times 10^{23}\ atoms/mol$, we get $N=5.58\times6.022\times 10^{23}\ atoms\approx3.36\times 10^{24}\ atoms$.