How much of a 5.2M sucrose solution should you use to make 81.0mL of a 0.040M solution?
c1v1 = c2v2
5.2M x v1 = 0.04 x 81.0
Solve for v1.
To solve this problem, we need to use the concept of molarity, which is the amount of solute (in moles) per unit volume of solution (in liters).
First, we need to calculate the number of moles of sucrose (C12H22O11) needed in the final solution.
To do this, we use the formula:
moles of solute = molarity × volume of solution (in liters)
Given:
Molarity of the final solution (M1) = 0.040M
Volume of the final solution (V1) = 81.0mL = 81.0/1000 = 0.081L
Molarity of the stock sucrose solution (M2) = 5.2M
Let's calculate the number of moles of sucrose needed:
moles of sucrose (C12H22O11) = Molarity × Volume
moles of sucrose (C12H22O11) = 0.040M × 0.081L
moles of sucrose (C12H22O11) = 0.00324 moles
Now, to find the volume of the 5.2M sucrose solution needed, we use the following formula:
Volume of stock solution (V2) = moles of solute (needed) / Molarity (of stock solution)
Volume of stock solution (V2) = 0.00324 moles / 5.2M
Volume of stock solution (V2) = 6.23 × 10^-4 L
Volume of stock solution (V2) = 6.23 × 10^-4 × 1000 mL
Volume of stock solution (V2) = 0.623 mL
Therefore, you would need to use approximately 0.623 mL of the 5.2M sucrose solution to make 81.0 mL of a 0.040M solution.