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, let's break it down step-by-step. We're aiming to find the weight of the substance needed to create a solution that meets the given dilution and concentration criteria.

### Step-by-step approach:

1. **Final concentration**: 
   We are given that 3 mL diluted to 100 mL results in a 1 in 5000 concentration. This means:
   \[
   \frac{\text{Amount of substance in 3 mL}}{100} = \frac{1}{5000}
   \]

   Rearranging:
   \[
   \text{Amount of substance in 3 mL} = \frac{100}{5000} = 0.02 \, \text{g}
   \]

   So, 3 mL of the product must contain 0.02 g of the substance.

2. **Concentration in 45 mL**:
   Now, we need to find how much substance is required for 45 mL of the product, keeping in mind that 3 mL should contain 0.02 g of the substance.

   The amount of substance in 1 mL is:
   \[
   \frac{0.02}{3} \, \text{g/mL}
   \]

   Therefore, the amount of substance required for 45 mL is:
   \[
   \text{Amount in 45 mL} = \frac{0.02}{3} \times 45
   \]
   \[
   \text{Amount in 45 mL} = 0.3 \, \text{g}
   \]

### Conclusion:
You would need **0.3 g** of the substance to make 45 mL of the product such that 3 mL diluted to 100 mL gives a 1 in 5000 concentration.

Would you like more details on any step? 

Here are some follow-up questions to consider:
1. How is concentration typically expressed in percentage form?
2. How would the calculations change if the dilution factor was different?
3. What is the importance of precise concentration in chemical formulations?
4. How does the density of the product affect the required weight of the substance?
5. What methods can be used to measure the weight of small quantities of a substance accurately?

**Tip**: Always double-check units to ensure they are consistent throughout your calculation process.

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?

Discover how to calculate the weight of a substance required to make 45mL of a product, ensuring that a 3mL portion diluted to 100mL results in a 1 in 5000 concentration. This detailed solution uses dilution and concentration concepts and is suitable for high school students.

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