Convert a density of 4.52 g/mL to its equivalent in kg/L.
The correct answer and explanation is :
Answer:
The given density is 4.52 g/mL. To convert this to kg/L, we use the conversion factors:
1 g = 0.001 kg
1 mL = 0.001 L
Since both gram-to-kilogram and milliliter-to-liter conversions involve multiplying by 0.001, they effectively cancel out, meaning:
[
4.52 \, g/mL = 4.52 \times \frac{0.001 \text{ kg}}{1 \text{ g}} \times \frac{1000 \text{ mL}}{1 \text{ L}}
]
[
= 4.52 \times 1 \text{ kg/L} = 4.52 \text{ kg/L}
]
Thus, 4.52 g/mL is equivalent to 4.52 kg/L.
Explanation:
Density is a measure of how much mass is contained in a given volume, commonly expressed in units like g/mL or kg/L. Since 1 mL = 1 cm³, the conversion from grams per milliliter (g/mL) to kilograms per liter (kg/L) relies on simple metric conversions.
The metric system makes this conversion straightforward because:
- 1 gram (g) is 1/1000 of a kilogram (kg)
- 1 milliliter (mL) is 1/1000 of a liter (L)
When converting from g/mL to kg/L, both the mass and volume conversions involve multiplying by 1000, which cancels out and leaves the numerical value unchanged.
This means that any density given in g/mL will have the same numerical value in kg/L because the conversion factors effectively cancel each other out.
For example:
- 1 g/mL = 1 kg/L
- 2.5 g/mL = 2.5 kg/L
- 4.52 g/mL = 4.52 kg/L
This principle applies universally, making conversions between these two units extremely simple in the metric system.
