Question

According to the escience lab manual for lab 1, experiment 3, you need to prepare a 47 mL of a 24% soda/syrup prescription. To do this, you can use the 80% syrup solution and the 10% soda solution that you have in stock. How many mLs of soda solution do you need to create this final solution?

Answer 1

33 mL

Step-by-step explanation:

It is important to recognize that the total amount of pure syrup remains constant:

Total syrup in the stock solution = total syrup in dilute solution

Thus, we can use the dilution formula

V₁c₁ = V₂ c₂

Data:

V₁ = ?; c₁ = 80 %

V₂ = 47 mL; c₂ = 24 %

Calculations:

1. The volume of stock syrup

`\begin{array}{rcl}V_(1)c_(1) & = & V_(2)c_(2)\\V_(1)*80 \, \% & = & \text{47 mL}* 24 \, \%\\80V_(1) & = & \text{1130 mL}\\V_(2)&=& \frac{\text{1130 mL}}{80}\\\\&=&\text{14 mL}\\\end{array}\\\text{You need $\textbf{14 mL}$ of stock syrup.}`

2. The volume of soda solution

Total volume of dilute solution = 47 mL

The volume of stock syrup = 14

Volume of soda solution = 33 mL

You need 33 mL of soda solution.