Prepare 50g of vanishing cream. Calculate how much water is needed to bring the total to 100g.
Understand the Problem
The question is asking for assistance in preparing a vanishing cream with specified ingredients and quantities. It involves calculations, particularly regarding the total weight to achieve and how much water should be added to reach that weight based on the given densities of glycerin and rose oil.
Answer
You need to add 25.3mL of water to achieve 50g of vanishing cream.
Answer for screen readers
The amount of water needed to prepare 50g of vanishing cream is 25.3g (or 25.3mL).
Steps to Solve
- Sum of the Ingredients Already Specified
First, we need to add the weights of the ingredients provided:
- Stearic acid = 17g
- Potassium Hydroxide (KOH) = 0.7g
- Glycerin = 5g
- Rose oil = 2g
Total weight of known ingredients: $$ \text{Total weight} = 17 + 0.7 + 5 + 2 = 24.7 \text{g} $$
- Calculate the Weight of Water Required
We want a total of 50g for the vanishing cream. So we need to find out how much water is needed to make up the difference:
$$ \text{Weight of water} = 50 - \text{Total weight of other ingredients} $$ $$ \text{Weight of water} = 50 - 24.7 = 25.3 \text{g} $$
- Convert the Weight of Water to Volume
To find the volume of water required, we use its density, which is approximately 1 g/mL. Thus, the volume in mL will be equal to the weight in grams:
$$ \text{Volume of water} = \text{Weight of water} \times \frac{1 \text{mL}}{1 \text{g}} $$ $$ \text{Volume of water} = 25.3 \text{mL} $$
The amount of water needed to prepare 50g of vanishing cream is 25.3g (or 25.3mL).
More Information
Vanishing cream is a mixture used in cosmetics that relies on a good balance between solid and liquid ingredients. The calculations help ensure precise formulation for consistency and effectiveness.
Tips
- Not summing ingredients correctly: Always double-check your addition to ensure accuracy.
- Confusing density: Remember, density varies for different substances; ensure you use the correct one for conversions.
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