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If the gasoline in a full 20.0-gallon tank weighs 116 pounds, what is the density of gasoline in grams per milliliter?

Answer :

To find the density of gasoline in grams per milliliter (g/mL), we need to follow these steps:

  1. Understand Density: Density is defined as mass divided by volume. The formula to calculate density is:

    [tex]\text{Density} = \frac{\text{Mass}}{\text{Volume}}[/tex]

  2. Convert Gallons to Liters: Since the weight of gasoline is given in pounds and the volume in gallons, we must convert gallons to liters because density in this case is needed in g/mL. We know that:

    • 1 gallon = 3.78541 liters
    • For a 20.0 gallon tank:

    [tex]20.0 \text{ gal} \times 3.78541 \text{ L/gal} \approx 75.7 \text{ L}[/tex]

  3. Convert Mass to Grams: We are given that the gasoline weighs 116 pounds. To convert pounds to grams, we use:

    • 1 pound = 453.592 grams
    • Therefore:

    [tex]116 \text{ lb} \times 453.592 \text{ g/lb} \approx 52,580.39 \text{ g}[/tex]

  4. Calculate Density: Now, we can plug these values into the density formula:

    [tex]\text{Density} = \frac{52,580.39 \text{ g}}{75.7 \text{ L}}[/tex] (Note: We will convert liters into milliliters in the calculation to get g/mL)

    • Since 1 L = 1000 mL, we have:

    [tex]75.7 \text{ L} \times 1000 \text{ mL/L} = 75,700 \text{ mL}[/tex]

    So the density calculation becomes:

    [tex]\text{Density} = \frac{52,580.39 \text{ g}}{75,700 \text{ mL}} \approx 0.6941 \text{ g/mL}[/tex]

  5. Conclusion: The density of gasoline in this example is approximately 0.694 g/mL. This density indicates how much mass is contained in a given volume of gasoline, which is a characteristic property of the substance.

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