### Introduction

The Inverse Stock Solution Makeup Calculator determines the amount of an additive required to yield a stock solution such that a specific volume of the solution will result in a desired increase in concentration of the additive in a specific volume of wine.

### Input Field Definitions

Total Solution Volume – The total volume of the stock solution being made.

Wine Volume – The volume of wine being treated.

Volume of Solution Added – The volume of stock solution to be added to the wine.

Total Dosage – The desired increase in concentration of the additive in the given volume of wine.

### Output Field Definitions

Mass of Additive Required – The mass of the additive required to make the given volume of stock solution.

### Calculation Details

This calculation determines the amount of a substance required to yield a stock solution such that a specific volume of the solution will result in a specific increase in concentration in a specific volume of wine, as described by Ben Rotter (2008).

The mass of the substance that we want to add to the wine is equal to the volume of the wine multiplied by the desired concentration increase in the wine, or:

m = _{w}v_{w}c_{w} |
(8-2) |

where:

*m _{w}* = mass of additive added to the wine, kg

*v _{w}* = wine volume, liters

*c _{w}* = concentration of the additive in the wine, kg/L

The mass of the substance to be added to the wine is also equal to the volume of the solution to be added to the wine multiplied by the concentration of the stock solution, or:

m = _{w}v_{a}c_{s} |
(8-3) |

where:

*v _{a}* = volume of the solution to be added to the wine, liters

*c _{s}* = concentration of the additive in the solution, kg/L

This mass of the additive required in the solution is the total volume of the solution multiplied by the concentration of the solution:

m = _{a}v_{s}c_{s} |
(8-4) |

Substituting equations 2 and 3 into equation 4 gives:

m = _{a}v / _{w}c_{w}v_{s}v_{a} |
(8-5) |