Diamond is pure carbon. Calculate the number of carbon atoms in 1.2 carat diamond. (1carat=0.200g)

To calculate the number of carbon atoms in a 1.2 carat diamond, we need to follow these steps:<br /><br />1. Convert the weight of the diamond from carats to grams.<br />2. Determine the number of moles of carbon in the diamond.<br />3. Calculate the number of carbon atoms using Avogadro's number.<br /><br />Let's go through each step:<br /><br />### Step 1: Convert Carats to Grams<br />Given:<br />\[ 1 \text{ carat} = 0.200 \text{ grams} \]<br /><br />For a 1.2 carat diamond:<br />\[ 1.2 \text{ carats} \times 0.200 \text{ grams/carats} = 0.24 \text{ grams} \]<br /><br />### Step 2: Determine the Number of Moles of Carbon<br />The molar mass of carbon (C) is approximately 12.01 grams per mole.<br /><br />\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]<br />\[ \text{Number of moles} = \frac{0.24 \text{ grams}}{12.01 \text{ grams/mole}} \]<br />\[ \text{Number of moles} \approx 0.02 \text{ moles} \]<br /><br />### Step 3: Calculate the Number of Carbon Atoms<br />Avogadro's number is \(6.022 \times 10^{23}\) atoms per mole.<br /><br />\[ \text{Number of atoms} = \text{number of moles} \times \text{Avogadro's number} \]<br />\[ \text{Number of atoms} = 0.02 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]<br />\[ \text{Number of atoms} \approx 1.2044 \times 10^{22} \text{ atoms} \]<br /><br />Therefore, a 1.2 carat diamond contains approximately \(1.2044 \times 10^{22}\) carbon atoms.