A recipe calls for 5M of sucrose (C12H22O11) dissolved in 750mL of H2O. Please calculate the total mass (g) of sucrose needed. Show all work.

Molarity x Volume in Liters = moles

mass(grams) = moles x formula weight

To calculate the total mass of sucrose needed, we need to use the given information: the molarity of sucrose and the volume of water.

First, let's convert the given volume of water from milliliters (mL) to liters (L):
750 mL ÷ 1000 = 0.75 L

Now, we can use the formula for molarity to find the number of moles of sucrose needed:
Molarity (M) = Moles of solute / Liters of solution

Rearranging the formula, we can solve for the moles of solute:
Moles of solute = Molarity (M) × Liters of solution

In this case, the molarity of sucrose is 5 M, and the volume of the solution is 0.75 L:
Moles of sucrose = 5 M × 0.75 L = 3.75 moles of sucrose

Next, we need to calculate the molar mass of sucrose. The molar mass of each element can be found on the periodic table:

C (carbon) = 12.01 g/mol
H (hydrogen) = 1.01 g/mol
O (oxygen) = 16.00 g/mol

Multiplying the atomic mass of each element by the number of atoms in the formula, we get:
12.01 g/mol × 12 (C) = 144.12 g/mol
1.01 g/mol × 22 (H) = 22.22 g/mol
16.00 g/mol × 11 (O) = 176.00 g/mol

Adding these values together gives us the molar mass of sucrose:
144.12 g/mol + 22.22 g/mol + 176.00 g/mol = 342.34 g/mol

Finally, we can calculate the total mass of sucrose needed by multiplying the number of moles by the molar mass:
Total mass of sucrose = Moles of sucrose × Molar mass of sucrose
Total mass of sucrose = 3.75 mol × 342.34 g/mol = 1285.775 g

Therefore, the total mass of sucrose needed is approximately 1285.775 grams.