Algebraic Method
If two or more solutions of different strengths are mixed to obtain a new mixture with a new strength, how do we calculate the new strength? These calculations can be performed by using either the algebraic method or the alligation method.
For the Algebraic method, the dilution equation can be modified as:
$$ V^1C^1 + V^2C^2 = V^n \times C^n $$
- V1 : volume of solution 1
- C1: concentration of solution 1
- V2 : volume of solution 2
- C2: concentration of solution 2
- Vn: final volume
- Cn: final concentration
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Solved Problem: In what proportions should 70 % dextrose and 10 % dextrose be mixed to make 1000 ml of 50 % dextrose? Approach: Using the above equation, let 70 % dextrose be solution 1 and 10 % be solution 2. Substituting the known values in to the equation, we get the following: $$ V^1(70) + (V^n - V^1)(10) = (1000) \times 50 $$ $$ V^1(70) + (1000 - V^1)(10) = (1000) \times 50 $$ $$ V^1(70) + 10000 - 10V^1 = 50000 $$ $$ 60V^1 = 40000 $$ $$ V^1 = { 40000 \over 60 } $$ $$ V^1 = {40000 \over 60} = 667 \ ml $$ $$ V^2 = {1000 - 667 \ ml} = 333 \ ml$$ Answer: Mix 667 ml of 70 % dextrose solution with 333 ml of 10 % dextrose solution to obtain 1000 ml of 50 % dextrose solution |
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Solved Problem: What is the concentration of a mixture of 100 g of a 20 % ointment, 500 g of 10 % ointment and 50 g of a 5 % ointment? Approach: use the equation: $$ V^1C^1 + V^2C^2 + V^3C^3 = V^n \times C^n $$ $$ 100 \times 20 + 400 \times 10 + 50 \times 5 = (100 + 500 + 50) \times C^n $$ $$ 2000 + 5000 + 250 = (650) \times C^n $$ $$ C^n = { 7250 \over 650 }$$ Answer: 11.2% |