22. You are conducting an experiment in the chemistry lab where you are tasked with identifying the sample that contains a specific number of atoms. As part of the experiment, you are given several samples of different substances, and you need to determine which sample contains exactly 9.0times 10^23atoms Which sample below contains a total of 9.0times 10^23 atoms? 1.5 moles of Cu 0.75 moles of H_(2)O 0.50 moles of HCI 1.5 moles of H_(2)

To determine which sample contains exactly \( 9.0 \times 10^{23} \) atoms, we need to calculate the total number of atoms in each given sample.<br /><br />1. **0.75 moles of \( \mathrm{H}_{2}\mathrm{O} \):**<br /><br /> Each molecule of water (\( \mathrm{H}_{2}\mathrm{O} \)) contains 3 atoms (2 hydrogen and 1 oxygen). Therefore, the total number of atoms in 0.75 moles of \( \mathrm{H}_{2}\mathrm{O} \) is calculated as follows:<br /><br /> \[<br /> \text{Total atoms} = 0.75 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \times 3 \, \text{atoms/molecule}<br /> \]<br /><br /> \[<br /> = 0.75 \times 6.022 \times 10^{23} \times 3<br /> \]<br /><br /> \[<br /> = 1.356 \times 10^{24} \, \text{atoms}<br /> \]<br /><br />2. **0.50 moles of HCl:**<br /><br /> Each molecule of HCl contains 2 atoms (1 hydrogen and 1 chlorine). Therefore, the total number of atoms in 0.50 moles of HCl is calculated as follows:<br /><br /> \[<br /> \text{Total atoms} = 0.50 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \times 2 \, \text{atoms/molecule}<br /> \]<br /><br /> \[<br /> = 0.50 \times 6.022 \times 10^{23} \times 2<br /> \]<br /><br /> \[<br /> = 6.022 \times 10^{23} \, \text{atoms}<br /> \]<br /><br />3. **1.5 moles of \( \mathrm{H}_{2} \):**<br /><br /> Each molecule of \( \mathrm{H}_{2} \) contains 2 atoms (both hydrogen). Therefore, the total number of atoms in 1.5 moles of \( \mathrm{H}_{2} \) is calculated as follows:<br /><br /> \[<br /> \text{Total atoms} = 1.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \times 2 \, \text{atoms/molecule}<br /> \]<br /><br /> \[<br /> = 1.5 \times 6.022 \times 10^{23} \times 2<br /> \]<br /><br /> \[<br /> = 1.8066 \times 10^{24} \, \text{atoms}<br /> \]<br /><br />Comparing these calculations with \( 9.0 \times 10^{23} \) atoms, none of the samples contain exactly \( 9.0 \times 10^{23} \) atoms. However, if you are looking for the closest match, the sample of 0.50 moles of HCl contains \( 6.022 \times 10^{23} \) atoms, which is less than \( 9.0 \times 10^{23} \), but it is the closest among the options provided.