The density of liquid mercury is 13.6 g/mL. What is its density in units of ? (2.54 cm = 1 in., 2.205 lb = 1 kg)
The Correct Answer and Explanation is:
To convert the density of liquid mercury from grams per milliliter (g/mL) to pounds per cubic inch (lb/in³), we need to use unit conversion factors.
Given Data:
- Density of liquid mercury = 13.6 g/mL
- Conversion factors:
- 1 inch = 2.54 cm
- 1 pound = 2.205 kg
- 1 kilogram = 1000 grams
- 1 mL = 1 cm³ (since 1 mL is equivalent to 1 cubic centimeter)
Step 1: Convert grams to pounds
We know that 1 kg = 1000 grams and 1 pound = 2.205 kg. First, let’s convert grams to pounds using these factors:
- 1 gram = 1/1000 kg
- 1 kg = 2.205 pounds
Therefore, the conversion factor from grams to pounds is:
11000×2.205=0.002205 lb/gram\frac{1}{1000} \times 2.205 = 0.002205 \text{ lb/gram}10001×2.205=0.002205 lb/gram
So, 13.6 grams = 13.6×0.002205=0.03004813.6 \times 0.002205 = 0.03004813.6×0.002205=0.030048 lb.
Step 2: Convert milliliters to cubic inches
1 mL is equivalent to 1 cm³, and we need to convert cubic centimeters (cm³) to cubic inches (in³). Using the fact that 1 inch = 2.54 cm, we can calculate the conversion factor for cubic volumes:(2.54 cm/in)3=16.387 cm3/in3(2.54 \, \text{cm/in})^3 = 16.387 \, \text{cm}^3/\text{in}^3(2.54cm/in)3=16.387cm3/in3
Therefore, 1 cm³ = 116.387\frac{1}{16.387}16.3871 in³ ≈ 0.061024 in³.
Step 3: Convert the density to lb/in³
Now, we can convert the density of mercury from g/mL to lb/in³. We multiply the density by the conversion factors for grams to pounds and milliliters to cubic inches:13.6 g/mL×0.002205 lb/g×10.061024 in3/mL13.6 \, \text{g/mL} \times 0.002205 \, \text{lb/g} \times \frac{1}{0.061024} \, \text{in}^3/\text{mL}13.6g/mL×0.002205lb/g×0.0610241in3/mL13.6×0.002205×16.387≈0.490 lb/in313.6 \times 0.002205 \times 16.387 \approx 0.490 \, \text{lb/in}^313.6×0.002205×16.387≈0.490lb/in3
Final Answer:
The density of liquid mercury is approximately 0.490 lb/in³.
This is the result of converting the given density from grams per milliliter to pounds per cubic inch using the appropriate conversion factors.
