Math Problem Statement

Suppose you have 2.50 L of a substance with a density of 9.00 g/mL and you want to determine the mass of the substance. The calculation can be broken down into three steps. First, convert the volume from liters to milliliters. Then, determine the mass of the sample in grams. Finally, convert the mass from grams to kilograms.

Solution

Let's walk through the problem step by step based on the image you provided:

Step 1:

  • You are asked to convert the volume from liters (L) to milliliters (mL).
  • The volume given is 2.50 L.

Since 1 L = 1000 mL, you can convert:

2.50L×1000mLL=2500mL2.50 \, L \times 1000 \, \frac{\text{mL}}{\text{L}} = 2500 \, \text{mL}

Step 2:

  • The next step is to convert milliliters (mL) to grams (g) using the density of the substance, which is 9.00 g/mL.

Multiply the volume (2500 mL) by the density:

2500mL×9.00gmL=22500g2500 \, \text{mL} \times 9.00 \, \frac{\text{g}}{\text{mL}} = 22500 \, \text{g}

Step 3:

  • Finally, convert the mass from grams (g) to kilograms (kg).
  • Since 1 kg = 1000 g, divide the mass by 1000:

22500g×1kg1000g=22.5kg22500 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 22.5 \, \text{kg}

Final Answer:

  • The mass of the substance is 22.5 kg.

Would you like to explore more details or have any questions?

Here are 5 follow-up questions you could consider:

  1. What is the relationship between liters and milliliters?
  2. How does density help in converting volume to mass?
  3. Why do we divide by 1000 when converting grams to kilograms?
  4. What would happen if the density of the substance was lower?
  5. Can you think of other examples where similar unit conversions are used?

Tip: Always check units when solving problems involving conversions to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Unit conversion
Density
Mass calculation

Formulas

1 L = 1000 mL
Mass = Volume × Density
1 kg = 1000 g

Theorems

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Suitable Grade Level

Grades 9-12