Example of an Ethanol Dilution

"You need to prepare 500 ml of 40 % Ethanol from Ethanol (96 per cent) BP. What volume of Ethanol (96 per cent) BP do you need?

The long approach uses the definition of percent volume in volume:

"Percent Volume in Volume gives the number of millilitres
of a component in 100 millilitres of the total system."

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Long Approach Using Definition of Percent Volume in Volume

"You need to prepare 500 ml of 40 % Ethanol from Ethanol (96 per cent) BP. What volume of Ethanol (96 per cent) BP do you need?

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Percent Volume in Volume gives the number of millilitres
of a component in 100 millilitres of the total system.
Find how many millilitres of Absolute Ethanol are needed in 500 ml
of 40 % v/v Ethanol.
A concentration of 40 % v/v means that:
100 ml of the solution contains 40 ml of Absolute Ethanol. Thus:
500 ml of the solution contains 500/100 x 40 ml = 200 ml of Absolute Ethanol.
Ethanol (96 per cent) BP contains 96.0 to 96.6 % Ethanol giving an average of 96.3 %.
Find what volume of Ethanol (96 per cent) BP contains 200 ml of Ethanol.
A concentration of 96.3 % means there are:
96.3 ml of Ethanol in every 100 ml of solution. Thus:
200 ml of Ethanol are in 200/96.3 x 100 ml
200 ml of Ethanol are in 207.7 ml of solution.
207.7 ml of Ethanol (96 per cent) BP are needed.
Formula:
207.7 ml Ethanol (96 per cent) BP to      500 ml Water
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The short approach uses the following equation:

Concentration1 x Quantity1 = Concentration2 x Quantity2

where:
Concentration1 = Concentration of Original Solution
Quantity1 = Quantity (mass or volume) of Original Solution
Concentration2 = Concentration of New Solution
Quantity2 = Quantity (mass of volume) of New Solution

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Derivation of the Equation

One definition of concentration expressed as a percent weight in volume is:

"Percent weight in volume is the mass - in grams - of a
component present in 100 millilitres of the total system"

This definition leads to the following equation:

Concentration % w/v = Mass (in grams) x           100          
Volume (in ml)

Now, for any dilution, the mass of the component stays the same:
you haven't added anymore of the component.

Rearranging the equations produces:
Concentration1 x Quantity1 = Concentration2 x Quantity2
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Rearranging the Equations

Before Dilution

Concentration1 = Mass x       100      
Quantity1
Concentration1 x Quantity1 = Mass x 100
Concentration1 x Quantity1 =

After Dilution

Concentration2 = Mass x       100      
Quantity2
Concentration2 x Quantity2 = Mass x 100
  Concentration2 x Quantity2

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Short Solution Using an Equation

"You need to prepare 500 ml of 40 % Ethanol from Ethanol (96 per cent) BP. What volume of Ethanol (96 per cent) BP do you need?

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The short approach uses a simple equation used for many dilution questions:
Concentration1 x Quantity1 = Concentration2 x Quantity2

Derivation of the Equation

One definition of concentration expressed as a percent weight in volume is:

"Percent weight in volume is the mass - in grams - of a
component present in 100 millilitres of the total system"

This definition leads to the following equation:

Concentration % w/v = Mass (in grams) x           100          
Volume (in ml)

Now, for any dilution, the mass of the component stays the same:
you haven't added anymore of the component.

Rearranging the equations produces:
Concentration1 x Quantity1 = Concentration2 x Quantity2
Click to Continue

Rearranging the Equations

Before Dilution

Concentration1 = Mass x       100      
Quantity1
Concentration1 x Quantity1 = Mass x 100
Concentration1 x Quantity1 =

After Dilution

Concentration2 = Mass x       100      
Quantity2
Concentration2 x Quantity2 = Mass x 100
  Concentration2 x Quantity2

Click to Continue
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You can solve this problem in two ways. The first approach is long and uses the definition of percent volume in volume. The second approach is shorter and uses a simple equation.