## Acid Titration Calculator

### Indroduction

The Acid Titration Calculator determines the titratable acidity (TA) of a wine sample given the volume of the sample and the volume of sodium hydroxide (NaOH) added during a titration test.

### Input Field Definitions

Wine Sample Volume – The volume of the wine sample being titrated.

Volume of NaOH Added – The volume of NaOH solution required to reach the titration endpoint.

NaOH Normality – The normality (moles/liter) of the NaOH solution used to titrate the wine sample.

### Output Field Definitions

Titratable Acidity (TA) – The calculated titratable acidity of the wine sample.

### Calculation Details

Acid titration makes use of the neutralization reaction between NaOH and the acids present in wine. In this reaction, the OH^{–} ions contributed by the NaOH and the H^{+} ions contributed by the wine acids combine to form water, H_{2}O. The reaction is complete when all of the H^{+} ions have been neutralized by OH^{–} ions. Since each OH^{–} ion neutralizes one H^{+} ion, we can write a balance between the H^{+} and OH^{–} ions as:

i(_{a}m/_{a}mw) = _{a}v _{n}N_{n} |
(1) |

where

i = number of H_{a}^{+} ions donated by each molecule of acidmw = molecular weight of acid, grams/mole_{a}m = mass of acid, grams_{a}v = volume of NaOH added, liters_{n}N = normality of NaOH solution, moles/liter_{n} |

The mass of the acid in solution is simply the acidity multiplied by the volume or:

m = _{a}a·v _{w} |
(2) |

where

a = acidity, grams/literv = volume of wine sample, liters _{w} |

Combining equations (1) and (2) and solving for acidity we get:

a = (mw/_{a}i)_{a}v / _{n}N_{n}v_{w} |
(3) |

By titrating for acidity, all we’ve really determined is the number of available H^{+} ions in the solution and not the types of acid present. For this reason we must choose an acid as a reference in order to express the acidity as a concentration. Tartaric acid is frequently used as a reference, and is the default acid reference in FermCalc. For tartaric acid, *mw _{a}* is 150.09, and

*i*is equal to 2, so equation (3) becomes:

_{a}a = 75.045·v / _{n}N_{n}v_{w} |
(4) |

## Acidification & Deacidification Calculator

### Indroduction

The Acidification & Deacidification Calculator determines the amount of a selected acid or deacidifier required to increase or decrease the acidity of a wine from its current value to some target value. If the target acidity is greater than the initial acidity, a list of acids will be shown. If the target acidity is less than the initial acidity, a list of deacidifiers will be shown.

Acid blend is assumed to be a blend of 40% tartaric, 40% malic, and 20% citric acids.

### Input Field Definitions

Target Acidity – The desired acidity of the wine.

Initial Acidity – The current acidity of the wine.

Wine Volume – The volume of wine being treated.

Acid Type – The acid to be used to treat the wine. The list of acids will be shown if the target acidity is greater than the initial acidity. Acid blend is assumed to be a blend of 40% tartaric, 40% malic, and 20% citric acids.

Deacidifier Type – The deacidifying agent to be used to treat the wine. The list of deacidifiers will be shown if the target acidity is less than the initial acidity.

### Output Field Definitions

Acid Required – The calculated mass of the selected acid required to achieve the target acidity.

Deacidifier Required – The calculated mass of the selected deacidifier required to achieve the target acidity.

### Calculation Details

There are two scenarios we need to consider for this calculation.

For the first scenario, FermCalc will calculate the amount of acid required to increase the acidity to the specified target. For the second case FermCalc will calculate the amount of deacidifier to add.

If you are diluting a must with water, blending juices, or blending wines to adjust acidity, use the Blending Calculator to calculate the proportions required to achieve the desired acidity.

#### Case 1: Initial Acidity is Less Than the Target Acidity

For this case we’ll be adding acid to increase the acidity. FermCalc first converts the initial and target acidity values to the tartaric reference using the conversion factors explained in the Acidity Conversions discussion.

To calculate the required addition of the selected acid we need to write a molar balance equation for the H^{+} ions in the wine. The final (or target) number of H^{+} ions must equal the initial number of H^{+} ions plus the number of H^{+} ions added, or:

i/_{t}a_{f}vmw = _{t}i/_{t}a_{i}vmw + _{t}i/_{a}m_{a}mw_{a} |
(5) |

where

i = number of H_{t}^{+} ions per molecule for tartaric acida = target (final) acidity, grams/liter tartaric_{f}a = initial acidity, grams/liter tartaric_{i}v = volume of wine, litersmw = molecular weight of tartaric acid, grams/mole_{t}i = number of H_{a}^{+} ions per molecule for the acid being addedm = mass of acid required, grams_{a}mw = molecular weight of the acid being added, grams/mole _{a} |

Rearranging to solve for the mass of acid to add we get:

m = _{a}v(a – _{f}a)(_{i}i/_{t}mw) / (_{t}i/_{a}mw)_{a} |
(6) |

Values of molecular weight and number of H^{+} ions per molecule are shown in the table below, compiled from Margalit (2004) and Weast (1977).

Acid | Molecular Weight | H^{+} Ions |
---|---|---|

Tartaric | 150.09 | 2 |

Malic | 134.09 | 2 |

Citric | 192.12 | 3 |

For Acid Blend, the composition is assumed to be 40% tartaric, 40% malic, and 20% citric acids.

#### Case 2: Initial Acidity is Greater Than the Target Acidity

For this case we’ll need to add a deacidifier such as calcium carbonate (CaCO_{3}), potassium carbonate (K_{2}CO_{3}), potassium bicarbonate (KHCO_{3}), or potassium hydroxide (KOH) to reduce the acidity. All of these work by neutralizing tartaric acid, or H_{2}T, where T represents a tartrate ion (C_{4}H_{4}O_{6}). The reaction equations are (Margalit, 2004 and Beelman et al., 1979):

CaCO_{3} + H_{2}T —> CaT + H_{2}O + CO_{2} |
(7) |

K_{2}CO_{3} + 2H_{2}T —> 2KHT + H_{2}O + CO_{2} |
(8) |

KHCO_{3} + H_{2}T —> KHT + H_{2}O + CO_{2} |
(9) |

KOH + H_{2}T —> KHT + H_{2}O |
(10) |

Note that KOH is not authorized by the Alcohol and Tobacco Tax and Trade Bureau (TTB) for treatment of wine or juice, so it cannot be used by commercial wineries. But that shouldn’t stop amateur winemakers from using it.

To calculate the required amount of any of these additives, we need to know their molecular weights as well as the number of H_{2}T molecules that are neutralized by each molecule of deacidifier. These parameters are tabulated below.

Deacidifier | Molecular Weight | Molecules of H_{2}TNeutralized |
---|---|---|

Calcium Carbonate | 100.09 | 1 |

Potassium Carbonate | 138.21 | 2 |

Potassium Bicarbonate | 100.12 | 1 |

Potassium Hydroxide | 56.106 | 1 |

We can calculate the required mass of deacidifier to add by balancing the initial and final quantities of H_{2}T molecules present against the number of molecules neutralized, or:

n·m/_{d}mw = _{d}v(a – _{i}a)/_{f}mw_{t} |
(11) |

where

n = molecules of H_{2}T neutralized per molecule of deacidifierm = mass of deacidifier added, grams_{d}mw = molecular weight of the deacidifier being added, grams/mole_{d}v = volume of wine, litersa = target (final) acidity, grams/liter tartaric_{f}a = initial acidity, grams/liter tartaric_{i}mw = molecular weight of tartaric acid, grams/mole _{t} |

Solving for the amount of acid reducer we get:

m = _{d}v(a – _{i}a)_{f}mw/(_{d}n·mw)_{t} |
(12) |

Based on equation 12 above, FermCalc calculates the following addition rates to reduce acidity by 0.1% (1 g/l) tartaric.

Calculated Addition Rates to Reduce Acidity by 0.1% (1 g/l) Tartaric | ||
---|---|---|

Deacidifier | grams/liter | grams/gallon(US) |

Calcium Carbonate | 0.67 | 2.52 |

Potassium Carbonate | 0.46 | 1.74 |

Potassium Bicarbonate | 0.67 | 2.53 |

Potassium Hydroxide | 0.37 | 1.42 |

For additional information on using these additives, see this article by Bill Collings.

## Amelioration Calculator

### Introduction

Amelioration is the dilution of must with water in order to reduce the acidity or sugar content. When diluting to reduce the acidity, it is often necessary to add sugar to maintain the potential alcohol level of the must. When diluting to reduce sugar content, it is often necessary to add acid to bring the acidity up to an acceptable level.

The Amelioration Calculator determines the required additions of water, sugar, and acid to a must to meet the desired acidity and SG levels given the initial acidity, initial SG, and initial must volume. Alternatively, the target must volume can be specified, in which case FermCalc calculates the initial volume of must required, along with the required water, acid, and sugar additions.

### Input Field Definitions

Acid Type – The type of acid being added, either tartaric, malic, citric, or acid blend. Acid blend is assumed to be a blend of 40% tartaric, 40% malic, and 20% citric acids.

Target Acidity – The desired acidity of the must after the water/sugar/acid additions. Range: 0 to 100 grams/liter.

Initial Acidity – The acidity of the must prior to the water/sugar/acid additions. Range: 0 to 100 grams/liter.

Target SG – The desired specific gravity of the must after the water/sugar/acid additions. Range: 0.77193 to 1.55454

Initial SG – The specific gravity of the must prior to the water/sugar/acid additions. Range: 0.77193 to 1.55454

Must Volume – The volume of the must prior to the water/sugar/acid additions.

Target Volume – The desired volume of the must after the water/sugar/acid additions.

### Output Field Definitions

Water Required – The volume of water required to meet the target acidity, SG, and volume.

Sugar Required – The mass of sugar required to meet the target acidity, SG, and volume.

Acid Required – The mass of acid required to meet the target acidity, SG, and volume.

Resulting Volume – The volume of the must after adding the water, sugar, and acid. Reported only if Must Volume is selected above.

Must Required – The volume of the juice required to meet the target acidity, SG, and volume. Reported only if Target Volume is selected above.

### Calculation Details

FermCalc first determines whether the acidity adjustment or the sugar adjustment requires the larger increase in volume. The increase in volume due to the acidity adjustment is calculated from the acid balance equation:

v = _{i}a_{i}v_{f}a_{f} |
(13) |

where:

v = initial must volume, liters_{i}v = final must volume, liters_{f}a = initial acidity, grams/liter tartaric_{i}a = final acidity, grams/liter tartaric_{f} |

Solving for *v _{f}* we get:

v = _{f}v / _{i}a_{i}a_{f} |
(14) |

Or if we’re solving for *v _{i}* we get:

v = _{i}v / _{f}a_{f}a_{i} |
(15) |

The increase in volume due to the sugar adjustment is calculated using the sugar mass balance equations:

v = _{f}sg_{f}ρ_{w}B_{f}v + _{i}sg_{i}ρ_{w}B_{i}m_{sa}B_{s} |
(16) |

v = _{f}sg_{f}ρ_{w}v + _{i}sg_{i}ρ_{w}m + _{sa}v_{wa}ρ_{w} |
(17) |

where:

v = initial must volume, liters_{i}v = final volume, liters_{f}sg = initial specific gravity_{i}sg = final specific gravity_{f}B = initial Brix_{i}B = final Brix_{f}B = sugar Brix_{s}ρ = density of water = 0.9982 kg/liter at 20ºC_{w}m = mass of sugar added, kg_{sa}v = volume of water added, liters _{wa} |

If the target (final) SG is greater than or equal to the initial SG, then we won’t be adding any water for the sugar adjustment, so *v _{wa}* is zero. If we solve equation (17) for

*m*, substitute it into equation (16), and re-arrange to solve for

_{sa}*v*, we get:

_{f}v = _{f}v(100 – _{i}sg_{i}B) / [_{i}sg(100 – _{f}B)]_{f} |
(18) |

Or if we’re solving for *v _{i}* we get:

v = _{i}v(100 – _{f}sg_{f}B) / [_{f}sg(100 – _{i}B)]_{i} |
(19) |

If the target SG is less than the initial SG, then we won’t be adding sugar, so *m _{sa}* is zero. Solving equation (16) for

*v*, we get:

_{f}v = (_{f}v) / (_{i}sg_{i}B_{i}sg)_{f}B_{f} |
(20) |

Or if we’re solving for *v _{i}* we get:

v = (_{i}v) / (_{f}sg_{f}B_{f}sg)_{i}B_{i} |
(21) |

The value of *v _{f}* is taken as the maximum value calculated by equations (14), (18), and (20). If we’re solving for

*v*, its value is taken as the minimum value calculated by equations (15), (19), and (21). Now that we know both

_{i}*v*and

_{i}*v*, we can solve equation (16) for the mass of sugar to add, or:

_{f}m = (_{sa}v – _{f}sg_{f} ρ_{w}B_{f}v)_{i}sg_{i}ρ_{w}B_{i} / 100 |
(22) |

Knowing the amount of sweetener to add we can then re-arrange equation (17) to solve for the amount of water to add:

v = (_{wa}v – _{f}sg_{f}ρ_{w}v – _{i}sg_{i}ρ_{w}m) / _{sa}ρ_{w} |
(23) |

The amount of acid to add is then calculated by modifying equation (6) above as:

m = (_{a}v – _{f}a_{f}v) (_{i}a_{i}i/_{t}mw) / (_{t}i/_{a}mw)_{a} |
(24) |

## NaOH Standardization Calculator

### Introduction

Standardization is the process of testing a solution of unknown concentration with a solution of a known, precise concentration. The NaOH Standardization Calculator determines the normality of your sodium hydroxide (NaOH) solution from the titration of a potassium hydrogen phthalate (KHP) solution of known normality.

There are a number good reasons to test your solution of sodium hydroxide (NaOH) prior to titrating your wine. First, NaOH solutions lose strength over time due to exposure to CO_{2} in the air. Second, NaOH solutions are virtually impossible to prepare to a precise molar concentration because the substance is hygroscopic (in other words, it absorbs moisture from the air) so a measured sample of the compound is never 100% NaOH. On the other hand, the acid salt potassium hydrogen phthalate, KHC_{8}H_{4}O_{4} or KHP, is not hygroscopic, so it can be measured out in precise mass amounts.

### Input Field Definitions

KHP Volume – The volume of KHP solution being titrated.

KHP Normality – The normality of the KHP solution being titrated.

Volume of NaOH Added – The volume of NaOH solution required to reach the titration endpoint.

### Output Field Definitions

NaOH Normality – The calculated normality of the NaOH solution.

### Calculation Details

The reaction equation for the standardization titration is.

KHC_{8}H_{4}O_{4} + NaOH —> KNaC_{8}H_{4}O_{4} + H_{2}O |
(25) |

Since KHP reacts with NaOH in a simple 1:1 stoichiometric ratio, we can write the following molar balance:

v = _{n}N_{n}v_{k}N_{k} |
(26) |

where

v = volume of NaOH sample, liters_{n}N = normality of NaOH sample, moles/liter_{n}v = volume of KHP sample, liters_{k}N = normality of KHP sample, moles/liter_{k} |

Rearranging equation (14) to solve for the NaOH normality gives:

N = _{n}v/_{k}N_{k}v_{n} |
(27) |

To perform the standardization titration, measure a small volume (5-10 mL) of the KPH into a water glass or flask. Add about 5 drops of phenolphthalein indicator to the sample. Titrate with your NaOH until the end is reached, which is the first pink blush that persists for at least 20 seconds after mixing the sample. Make note of how much NaOH was used, and enter the values into FermCalc to determine the normality of your NaOH.