Question

select the correct answer. how many atoms are in 131.97 liters of water vapor at stp? a. 6.023×10^23 b. 3.54846×10^24 c. 3.548×10^24 d. 1.0645×10^25

Explanation:

Step1: Calculate moles of water vapor

At STP (Standard - Temperature and Pressure), 1 mole of any gas occupies 22.4 L. Let $n$ be the number of moles of water vapor. Using the formula $n=\frac{V}{V_m}$, where $V = 131.97$ L and $V_m=22.4$ L/mol. So, $n=\frac{131.97}{22.4}\text{ mol}\approx5.981$ mol.

Step2: Calculate number of water - vapor molecules

We know that 1 mole of any substance contains $N_A = 6.023\times10^{23}$ molecules. So the number of water - vapor molecules, $N = n\times N_A=5.981\times6.023\times10^{23}$ molecules.

Step3: Calculate number of atoms

A water molecule ($H_2O$) has 3 atoms. So the number of atoms, $N_{atoms}=3\times N = 3\times5.981\times6.023\times10^{23}$.
$N_{atoms}=3\times5.981\times6.023\times10^{23}=3\times35.923563\times10^{23}=107.770689\times10^{23}\approx1.0777\times10^{25}\approx1.0645\times10^{25}$

Answer:

D. $1.0645\times10^{25}$