It is necessary to make 2000 kg / h of yogurt whose concentration of lactic acid (C3H6O3) is 0.8%.
The reactions that account for the process are the following:
C12H22O11 + H2O -----> C6H12O6
C6H12O6 + Microorganisms -----> C3 H6O3
Determine the amount of milk to obtain this acidity if we start with milk that has 48.5 g of lactose per kilogram of milk, assuming that all the lactose is transformed into lactic acid.
To determine the amount of milk needed to obtain the desired amount of lactic acid, we need to calculate the amount of lactose present in the milk.
Given that the milk has 48.5 g of lactose per kilogram of milk, we can calculate the lactose content in 2000 kg of milk.
Lactose content in 2000 kg of milk = 48.5 g/kg * 2000 kg = 97,000 g = 97 kg
Since lactose is transformed into lactic acid, the amount of lactic acid produced will be equal to the amount of lactose present in the milk.
Therefore, the amount of milk needed to obtain 2000 kg/h of yogurt with a concentration of 0.8% lactic acid is 97 kg.
To determine the amount of milk required to obtain the desired acidity, we need to calculate the amount of lactose present in the milk that will be converted into lactic acid.
Given:
Desired lactic acid concentration = 0.8%
Initial lactose concentration in milk = 48.5 g/kg
Step 1: Calculate the molar mass of lactose (C12H22O11):
- Molar mass of C = 12.01 g/mol
- Molar mass of H = 1.008 g/mol
- Molar mass of O = 16.00 g/mol
Molar mass of lactose = (12.01 * 12) + (1.008 * 22) + (16.00 * 11) = 342.30 g/mol
Step 2: Convert the desired lactic acid concentration to grams per liter:
- Desired lactic acid concentration = 0.8% = 0.8 g per 100 ml
- 0.8 g per 100 ml * 10 = 8 g per liter
Step 3: Calculate the amount of lactose needed:
- Since 1 mole of lactose yields 2 moles of lactic acid (from the balanced equation), the molar ratio is 2:1.
- Therefore, to produce 8 g of lactic acid, we need 4 g of lactose.
Step 4: Determine the amount of milk required to obtain this amount of lactose:
- We know that the initial lactose concentration in milk is 48.5 g/kg, so we can set up a proportion:
48.5 g of lactose / 1000 g of milk = 4 g of lactose / x g of milk
Cross-multiplying and solving for x, we get:
x = (4 g of lactose * 1000 g of milk) / 48.5 g of lactose
x ≈ 82.47 g of milk
Therefore, approximately 82.47 g of milk is required to obtain 2000 kg/h of yogurt with a lactic acid concentration of 0.8%, assuming all the lactose is converted into lactic acid.