A recipe calls for 45 dag of calcium chloride 25% w/w (SG = 1.23). How many centiliters
of calcium chloride 20% w/v would need to be used for this recipe?

To solve this problem, we need to find the volume (in centiliters) of a 20% w/v (weight/volume) calcium chloride solution that contains the same amount of calcium chloride as 45 dag (decagrams) of a 25% w/w (weight/weight) solution.

### Step-by-Step Solution:

1. **Convert 45 dag to grams:**

   Since 1 dag (decagram) is equal to 10 grams:
   \[
   45 \, \text{dag} = 45 \times 10 = 450 \, \text{g}
   \]

2. **Calculate the mass of calcium chloride in the 25% w/w solution:**

   A 25% w/w solution means that there are 25 grams of calcium chloride per 100 grams of solution. So, for 450 grams of solution:

   \[
   \text{Mass of CaCl}_2 = 450 \, \text{g} \times \frac{25}{100} = 112.5 \, \text{g}
   \]

   This means the solution contains 112.5 grams of calcium chloride.

3. **Determine the required volume of 20% w/v solution:**

   A 20% w/v solution means there are 20 grams of calcium chloride per 100 milliliters (or 10 centiliters) of solution. We want to find out how many centiliters (cl) of this solution are needed to obtain 112.5 grams of calcium chloride.

   Let \( V \) be the volume in centiliters.

   \[
   \text{Concentration (w/v)} = \frac{\text{Mass of solute}}{\text{Volume of solution in cl}} \times 10
   \]

   For a 20% w/v solution, we can set up the equation:

   \[
   20 = \frac{112.5}{V} \times 10
   \]

   Solving for \( V \):

   \[
   V = \frac{112.5 \times 10}{20} = 56.25 \, \text{cl}
   \]

### Conclusion:

You would need **56.25 centiliters** of the 20% w/v calcium chloride solution for the recipe.

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Do you want further details or have any questions? Here are 5 related questions that expand on this information:

1. How would the calculation change if the solution concentration was given in molarity (M) instead of percentage?
2. How do you convert between weight/volume and weight/weight concentrations?
3. What is the significance of specific gravity (SG) in calculating solution concentrations?
4. How would you calculate the mass of solvent required in a given solution concentration?
5. What are common applications of calcium chloride in recipes or chemical processes?

**Tip:** When working with different types of concentrations (w/w,

A recipe calls for 45 dag of calcium chloride 25% w/w (SG = 1.23). How many centiliters of calcium chloride 20% w/v would need to be used for this recipe?

Learn how to calculate the required volume of a 20% w/v calcium chloride solution when given 45 dag of a 25% w/w calcium chloride solution. This problem includes key concepts in concentration, unit conversion, and proportional reasoning. Suitable for students in Grades 11-12.

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