Question

1. which sample contains a total of $9.0 \times 10^{23}$ atoms?

\bigcirc 0.50 mole of hcl
\bigcirc 0.75 mole of $h_2o$
\bigcirc 1.5 moles of cu
\bigcirc 1.5 moles of $h_2$
clear all

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \(6.02\times 10^{23}\) particles per mole. For each compound, we need to calculate the total number of atoms.

Step2: Analyze 0.50 mole of HCl

HCl has 2 atoms per molecule (H and Cl). Number of molecules: \(0.50\ mol\times6.02\times 10^{23}\ mol^{-1}=3.01\times 10^{23}\) molecules. Total atoms: \(3.01\times 10^{23}\times2 = 6.02\times 10^{23}\) atoms. Not \(9.0\times 10^{23}\).

Step3: Analyze 0.75 mole of \(H_2O\)

\(H_2O\) has 3 atoms per molecule (2 H, 1 O). Number of molecules: \(0.75\ mol\times6.02\times 10^{23}\ mol^{-1}=4.515\times 10^{23}\) molecules. Total atoms: \(4.515\times 10^{23}\times3 = 1.3545\times 10^{24}\) atoms. Not \(9.0\times 10^{23}\).

Step4: Analyze 1.5 moles of Cu

Cu is a single - atom element. Number of atoms: \(1.5\ mol\times6.02\times 10^{23}\ mol^{-1}=9.03\times 10^{23}\approx9.0\times 10^{23}\) atoms.

Step5: Analyze 1.5 moles of \(H_2\)

\(H_2\) has 2 atoms per molecule. Number of molecules: \(1.5\ mol\times6.02\times 10^{23}\ mol^{-1}=9.03\times 10^{23}\) molecules. Total atoms: \(9.03\times 10^{23}\times2 = 1.806\times 10^{24}\) atoms. Not \(9.0\times 10^{23}\).

Answer:

1.5 moles of Cu