7. A silver charm has a mass of 25 .0 grams. How many atoms of silver are there? 8. What is heavier a mole of water or a mole of carbon dioxide; show proof to back up your claim. 9. How heavy (in grams) will 6.14times 10^25 atoms of gold be?

7. To find the number of atoms of silver in a silver charm with a mass of 25.0 grams, we need to use the molar mass of silver and Avogadro's number.<br /><br />The molar mass of silver (Ag) is 107.87 g/mol. This means that 1 mole of silver has a mass of 107.87 grams.<br /><br />Avogadro's number is 6.022 x 10^23 atoms/mol. This means that 1 mole of any substance contains 6.022 x 10^23 atoms.<br /><br />To find the number of atoms of silver in the silver charm, we can use the following steps:<br /><br />1. Convert the mass of the silver charm to moles:<br /> Mass of silver charm = 25.0 grams<br /> Molar mass of silver = 107.87 g/mol<br /> Moles of silver = Mass of silver charm / Molar mass of silver<br /> Moles of silver = 25.0 grams / 107.87 g/mol = 0.2306 moles<br /><br />2. Convert the moles of silver to the number of atoms:<br /> Number of atoms = Moles of silver x Avogadro's number<br /> Number of atoms = 0.2306 moles x 6.022 x 10^23 atoms/mol = 1.39 x 10^23 atoms<br /><br />Therefore, there are approximately 1.39 x 10^23 atoms of silver in the silver charm.<br /><br />8. To determine which is heavier, a mole of water or a mole of carbon dioxide, we need to compare their molar masses.<br /><br />The molar mass of water (H2O) is 18.015 g/mol, which means that 1 mole of water has a mass of 18.015 grams.<br /><br />The molar mass of carbon dioxide (CO2) is 44.01 g/mol, which means that 1 mole of carbon dioxide has a mass of 44.01 grams.<br /><br />Since the molar mass of carbon dioxide (44.01 g/mol) is greater than the molar mass of water (18.015 g/mol), a mole of carbon dioxide is heavier than a mole of water.<br /><br />Proof:<br />Molar mass of carbon dioxide (CO2) = 44.01 g/mol<br />Molar mass of water (H2O) = 18.015 g/mol<br /><br />Since 44.01 g/mol > 18.015 g/mol, a mole of carbon dioxide is heavier than a mole of water.<br /><br />9. To find the mass of $6.14\times 10^{25}$ atoms of gold, we need to use the molar mass of gold and Avogadro's number.<br /><br />The molar mass of gold (Au) is 197.0 g/mol. This means that 1 mole of gold has a mass of 197.0 grams.<br /><br />Avogadro's number is 6.022 x 10^23 atoms/mol. This means that 1 mole of any substance contains 6.022 x 10^23 atoms.<br /><br />To find the mass of $6.14\times 10^{25}$ atoms of gold, we can use the following steps:<br /><br />1. Convert the number of atoms to moles:<br /> Number of atoms = $6.14\times 10^{25}$<br /> Avogadro's number = 6.022 x 10^23 atoms/mol<br /> Moles of gold = Number of atoms / Avogadro's number<br /> Moles of gold = $6.14\times 10^{25}$ atoms / 6.022 x 10^23 atoms/mol = 102.3 moles<br /><br />2. Convert the moles of gold to the mass:<br /> Molar mass of gold = 197.0 g/mol<br /> Mass of gold = Moles of gold x Molar mass of gold<br /> Mass of gold = 102.3 moles x 197.0 g/mol = 20156.1 grams<br /><br />Therefore, $6.14\times 10^{25}$ atoms of gold will have a mass of 20156.1 grams.