You have a tank of wine that needs a 20 ppm addition of SO2.
Answer the following questions.
1. To make 5 gallons of a 6% w/v SO2 solution (expressed as SO2) how much K2S2O5 (222 g/mol) should be weighed out?
2. How much of this solution (in mLs) should be added to the tank (wine is 73 inches high in the tank, 11.4 gallons/inch)?
To find the answers to these questions, we need to use some basic calculations and formulas. Let's break it down step by step.
1. To make a 6% w/v (weight/volume) solution of SO2, we need to calculate the amount of K2S2O5 required.
The formula to calculate the amount of a solute needed is:
Amount of solute (in grams) = Concentration (in g/L) × Volume of solution (in L)
Given:
- Concentration of SO2 solution desired: 6% w/v
- Volume of solution desired: 5 gallons
First, we need to convert the volume from gallons to liters. One gallon is approximately equal to 3.78541 liters, so:
Volume of solution (in L) = 5 gallons × 3.78541 L/gallon = <<5*3.78541=18.92705>>18.92705 L
Next, it is important to note that a 6% w/v solution means 6 grams of solute per 100 mL of solution. Therefore, 6% w/v is equivalent to 60 g/L.
Using the formula, we can calculate the amount of K2S2O5 needed:
Amount of K2S2O5 (in grams) = Concentration (in g/L) × Volume of solution (in L)
Amount of K2S2O5 = 60 g/L × 18.92705 L = <<60*18.92705=1135.623>>1135.623 g
Therefore, you will need to weigh out approximately 1135.623 grams of K2S2O5 to make a 5-gallon solution with a 6% w/v concentration of SO2.
2. To determine how much of this solution (in mL) should be added to the tank, we need to consider the desired addition of 20 ppm (parts per million) of SO2 and the dimensions of the tank.
Given:
- Desired addition of SO2: 20 ppm
- Height of the tank: 73 inches
- Conversion rate of 11.4 gallons per inch
First, we need to convert the height of the tank from inches to gallons:
Volume of tank (in gallons) = Height of tank (in inches) × Conversion rate (gallons/inch)
Volume of tank = 73 inches × 11.4 gallons/inch = 832.2 gallons
Next, we need to calculate the total amount of SO2 needed for the tank:
Amount of SO2 (in gallons) = 832.2 gallons × (20 ppm / 1,000,000)
Amount of SO2 = 0.016644 gallons
Finally, we can calculate the volume of the 6% w/v SO2 solution needed:
Volume of 6% SO2 solution (in mL) = Amount of SO2 (in gallons) × 1000 mL/gallon
Volume of 6% SO2 solution = 0.016644 gallons × 1000 mL/gallon = 16.644 mL
Therefore, you should add approximately 16.644 mL of the 6% w/v SO2 solution to the tank to achieve a 20 ppm addition of SO2.