How many molecules are there in 122 grams of Cu(NO_(3))_(2)

To find the number of molecules in 122 grams of $Cu(NO_{3})_{2}$, we need to follow these steps:<br /><br />1. Calculate the molar mass of $Cu(NO_{3})_{2}$.<br />2. Convert the given mass of $Cu(NO_{3})_{2}$ to moles.<br />3. Use Avogadro's number to find the number of molecules.<br /><br />Step 1: Calculate the molar mass of $Cu(NO_{3})_{2}$.<br />The molar mass of $Cu(NO_{3})_{2}$ is the sum of the molar masses of its constituent atoms:<br />- Copper (Cu): 63.55 g/mol<br />- Nitrogen (N): 14.01 g/mol<br />- Oxygen (O): 16.00 g/mol<br /><br />Molar mass of $Cu(NO_{3})_{2}$ = 63.55 + (2 × 14.01) + (6 × 16.00) = 187.57 g/mol<br /><br />Step 2: Convert the given mass of $Cu(NO_{3})_{2}$ to moles.<br />Given mass of $Cu(NO_{3})_{2}$ = 122 grams<br /><br />Moles of $Cu(NO_{3})_{2}$ = Given mass / Molar mass<br />Moles of $Cu(NO_{3})_{2}$ = 122 g / 187.57 g/mol = 0.651 moles<br /><br />Step 3: Use Avogadro's number to find the number of molecules.<br />Avogadro's number = $6.022 \times 10^{23}$ molecules/mol<br /><br />Number of molecules = Moles × Avogadro's number<br />Number of molecules = 0.651 moles × $6.022 \times 10^{23}$ molecules/mol<br />Number of molecules = $3.92 \times 10^{23}$ molecules<br /><br />Therefore, there are approximately $3.92 \times 10^{23}$ molecules in 122 grams of $Cu(NO_{3})_{2}$.