Find the mass in grams of 2.00times 10^23 molecules of Cl_(2)

To find the mass in grams of $2.00\times 10^{23}$ molecules of $Cl_{2}$, we need to follow these steps:<br /><br />1. Determine the molar mass of $Cl_{2}$.<br />2. Calculate the number of moles of $Cl_{2}$ using Avogadro's number.<br />3. Multiply the number of moles by the molar mass to find the mass in grams.<br /><br />Step 1: Determine the molar mass of $Cl_{2}$.<br />The molar mass of chlorine (Cl) is approximately 35.45 g/mol. Since $Cl_{2}$ consists of two chlorine atoms, the molar mass of $Cl_{2}$ is:<br />\[ \text{Molar mass of } Cl_{2} = 2 \times 35.45 \, \text{g/mol} = 70.90 \, \text{g/mol} \]<br /><br />Step 2: Calculate the number of moles of $Cl_{2}$ using Avogadro's number.<br />Avogadro's number is $6.022 \times 10^{23}$ molecules/mol. To find the number of moles, we divide the given number of molecules by Avogadro's number:<br />\[ \text{Number of moles} = \frac{2.00 \times 10^{23} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mol}} \approx 0.332 \, \text{mol} \]<br /><br />Step 3: Multiply the number of moles by the molar mass to find the mass in grams.<br />\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]<br />\[ \text{Mass} = 0.332 \, \text{mol} \times 70.90 \, \text{g/mol} \approx 23.50 \, \text{g} \]<br /><br />Therefore, the mass of $2.00\times 10^{23}$ molecules of $Cl_{2}$ is approximately 23.50 grams.