What weight of a substance is required to make 45mL of a
product such that 3mL diluted to 100mL will give a 1 in 5000
concentration ?

To solve this problem, we can break it down into steps:

### Step 1: Understand the target concentration
The goal is to have a final concentration where 3 mL of the substance, when diluted to 100 mL, results in a 1 in 5000 concentration. This means that after dilution, the concentration of the substance in the solution will be:

\[
\frac{1}{5000} \text{ grams per mL}
\]

This corresponds to a concentration of:
\[
\frac{1}{5000} = 0.0002 \text{ g/mL}
\]

So, the final concentration in the diluted solution (after diluting 3 mL to 100 mL) is 0.0002 g/mL.

### Step 2: Calculate the amount of substance in 100 mL
If the final concentration is 0.0002 g/mL, the total amount of substance in 100 mL of the solution is:

\[
\text{Amount of substance} = 0.0002 \, \text{g/mL} \times 100 \, \text{mL} = 0.02 \, \text{g}
\]

### Step 3: Calculate the concentration in 3 mL before dilution
The 0.02 g of the substance is contained in the 3 mL of the undiluted solution (before being diluted to 100 mL). Thus, the concentration in this 3 mL of solution is:

\[
\text{Concentration in 3 mL} = \frac{0.02 \, \text{g}}{3 \, \text{mL}} = 0.00667 \, \text{g/mL}
\]

### Step 4: Calculate the concentration needed in the 45 mL product
The entire 45 mL product will have the same concentration as the 3 mL sample. Therefore, the concentration of the substance in the 45 mL product needs to be:

\[
0.00667 \, \text{g/mL}
\]

### Step 5: Calculate the total amount of substance required in the 45 mL
To find the total weight of the substance needed for the 45 mL product, multiply the concentration by the volume:

\[
\text{Total weight of substance} = 0.00667 \, \text{g/mL} \times 45 \, \text{mL} = 0.30015 \, \text{g}
\]

### Conclusion:
The weight of the substance required to make 45 mL of the product is approximately **0.30015 grams**.

Would you like further clarification on any part of this solution? Here are some related questions:

1. How do you adjust if the product volume is different?
2. What if the concentration required is 1 in 10,000 instead of 1 in 5000?
3. How would you calculate if the dilution factor changes?
4. Can you explain more about dilutions and concentration calculations?
5. How would this apply to liquid medications or chemical preparations?

**Tip:** Always make sure to keep track of units when performing dilution and concentration calculations to avoid errors.

What weight of a substance is required to make 45mL of a product such that 3mL diluted to 100mL will give a 1 in 5000 concentration?

Learn how to calculate the weight of a substance needed to make 45 mL of a product, ensuring that 3 mL diluted to 100 mL results in a 1 in 5000 concentration. This detailed solution covers concentration, dilution, and algebraic calculations, making it suitable for high school students (Grades 10-12).

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