What is the density of a mystery liquid in g per mL if 65.0 fluid ounces weighs 202 mass ounces?
The correct answer and explanation is :
Density Calculation and Explanation
Step 1: Understanding the Density Formula
Density ((\rho)) is the mass per unit volume and is calculated using the formula:
[
\rho = \frac{\text{Mass}}{\text{Volume}}
]
Given:
- Mass = 202 ounces (oz)
- Volume = 65.0 fluid ounces (fl oz)
Since we need the density in grams per milliliter ((\text{g/mL})), we need to convert the given values into appropriate units.
Step 2: Converting Mass to Grams
We use the conversion factor:
[
1 \text{ ounce (mass)} = 28.3495 \text{ grams}
]
[
202 \text{ oz} \times 28.3495 \text{ g/oz} = 5,728.39 \text{ g}
]
Step 3: Converting Volume to Milliliters
We use the conversion factor:
[
1 \text{ fluid ounce} = 29.5735 \text{ mL}
]
[
65.0 \text{ fl oz} \times 29.5735 \text{ mL/fl oz} = 1,922.28 \text{ mL}
]
Step 4: Calculating Density
Now, we divide mass by volume:
[
\rho = \frac{5,728.39 \text{ g}}{1,922.28 \text{ mL}}
]
[
\rho = 2.98 \text{ g/mL}
]
Explanation (300 Words)
The density of a substance is a measure of how much mass it contains in a given volume. It is typically expressed in grams per milliliter (g/mL) for liquids. In this problem, we are given the mass and volume in ounces, so we must convert them into standard metric units to determine the density correctly.
First, we convert mass from ounces to grams using the known conversion factor (1 oz = 28.3495 g). Multiplying the given mass (202 oz) by this factor, we find the total mass in grams.
Next, we convert the volume from fluid ounces to milliliters using the conversion factor (1 fl oz = 29.5735 mL). Multiplying the given volume (65.0 fl oz) by this factor gives the volume in milliliters.
Once we have mass in grams and volume in milliliters, we apply the density formula. Dividing the total mass by the total volume gives a density of 2.98 g/mL.
This density is significantly higher than that of water (1.00 g/mL), suggesting the mystery liquid is denser than water. This could indicate a heavy liquid like syrup, oil, or another dense chemical compound.
Understanding density is crucial in various scientific and industrial applications, including material identification, quality control, and fluid dynamics.