To prepare 500 mL of D12.5W using D70 and sterile water, how much SWFI is needed?

To arrive at the correct volume of sterile water for injection (SWFI) needed to prepare 500 mL of a 12.5% dextrose solution (D12.5W) using a 70% dextrose solution (D70), it's essential to use the concept of concentration and dilution.

The formula to determine the volumes of two solutions mixed to achieve a desired concentration can be framed using the equation:

C1V1 + C2V2 = CfVf,

where C refers to concentration, V refers to volume, and the subscripts refer to the initial solutions and final solution.

In this context:

• C1 is the concentration of D70 (which is 70% or 0.7 as a decimal),

• V1 is the volume of D70 that you will determine,

• C2 is the concentration of SWFI (which is 0% dextrose, or 0 as a decimal),

• V2 is the volume of SWFI,

• Cf is the desired concentration (12.5% or 0.125),

• Vf is the final volume (500 mL).

To solve for V1 (the volume of D70) and V2