A pharmacist weighs out 2 kg of glycerin ( density 1.25 g / ml ) . Calculate for the volume of glycerin?
The correct answer and explanation is:
To calculate the volume of glycerin from its mass and density, we use the formula: Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}
🔢 Step-by-step Solution:
Given:
- Mass of glycerin = 2 kg = 2000 grams (since 1 kg = 1000 grams)
- Density of glycerin = 1.25 g/mL
Now plug into the formula: Volume=2000 g1.25 g/mL=1600 mL\text{Volume} = \frac{2000\ \text{g}}{1.25\ \text{g/mL}} = 1600\ \text{mL}
✅ Final Answer:
Volume = 1600 mL
or
1.6 Liters (since 1000 mL = 1 Liter)
📘 300-Word Explanation:
To solve this problem, we need to understand the relationship between mass, density, and volume. These three are connected through the formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}
If you rearrange this formula to solve for volume, you get: Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}
In the context of this problem, a pharmacist is weighing out 2 kilograms of glycerin. Since the given density is in grams per milliliter (g/mL), we must convert kilograms to grams to match the units: 2 kg=2000 grams2\ \text{kg} = 2000\ \text{grams}
Now we substitute into the formula using the given density of 1.25 g/mL: Volume=20001.25=1600 mL\text{Volume} = \frac{2000}{1.25} = 1600\ \text{mL}
This tells us that 2000 grams (or 2 kg) of glycerin occupies 1600 milliliters of volume. For convenience, since pharmacists often work in liters, we can convert milliliters to liters: 1600 mL=1.6 L1600\ \text{mL} = 1.6\ \text{L}
Understanding this relationship is vital in pharmacy and chemistry, where accurate measurement of liquids based on their mass and density ensures proper formulation and dosing. This calculation is a common example of dimensional analysis used in real-world scientific applications.