4. If you have 2.5times 10^22 molecules of glucose (C_(6)H_(12)O_(6)) , how much does this amount weigh in grams?

To find the weight of $2.5\times 10^{22}$ molecules of glucose in grams, we need to follow these steps:<br /><br />1. Calculate the molar mass of glucose (C6H12O6).<br />2. Convert the number of molecules to moles.<br />3. Convert the number of moles to grams.<br /><br />Step 1: Calculate the molar mass of glucose (C6H12O6).<br />The molar mass of glucose is calculated by adding the molar masses of its constituent elements:<br />- Carbon (C): 12.01 g/mol<br />- Hydrogen (H): 1.01 g/mol<br />- Oxygen (O): 16.00 g/mol<br /><br />Molar mass of glucose = (6 × 12.01) + (12 × 1.01) + (6 × 16.00) = 180.16 g/mol<br /><br />Step 2: Convert the number of molecules to moles.<br />To convert the number of molecules to moles, we use Avogadro's number, which is $6.022\times 10^{23}$ molecules/mol.<br /><br />Number of moles = $\frac{2.5\times 10^{22}}{6.022\times 10^{23}}$ = 0.415 moles<br /><br />Step 3: Convert the number of moles to grams.<br />To convert the number of moles to grams, we multiply the number of moles by the molar mass of glucose.<br /><br />Weight in grams = 0.415 moles × 180.16 g/mol = 74.5 grams<br /><br />Therefore, $2.5\times 10^{22}$ molecules of glucose weigh approximately 74.5 grams.