Glycerin has a specific gravity of 1.258. How much would 50 gal of glycerin weigh?
The correct answer and explanation is :
Sure! Let’s start with the calculation and then I’ll explain the details.
Given:
- Specific gravity (SG) of glycerin = 1.258
- Volume of glycerin = 50 gallons
Step 1: Understand specific gravity
Specific gravity is the ratio of the density of a substance to the density of water at 4°C (which is approximately 1 g/cm³ or 62.4 lb/ft³). Since SG is dimensionless: Density of glycerin=SG×Density of water\text{Density of glycerin} = \text{SG} \times \text{Density of water}
Step 2: Density of water in consistent units
Water density is commonly used as:
- 62.4 lb/ft³ (pounds per cubic foot)
- 8.34 lb/gal (pounds per gallon)
Since volume is given in gallons, let’s use pounds per gallon for simplicity: Density of water=8.34lbgal\text{Density of water} = 8.34 \frac{\text{lb}}{\text{gal}}
Step 3: Calculate density of glycerin
Density of glycerin=1.258×8.34=10.49lbgal\text{Density of glycerin} = 1.258 \times 8.34 = 10.49 \frac{\text{lb}}{\text{gal}}
Step 4: Calculate the weight of 50 gallons of glycerin
Weight=Volume×Density=50 gal×10.49lbgal=524.5 lb\text{Weight} = \text{Volume} \times \text{Density} = 50 \, \text{gal} \times 10.49 \frac{\text{lb}}{\text{gal}} = 524.5 \, \text{lb}
Answer:
The weight of 50 gallons of glycerin is 524.5 pounds.
Explanation (300 words)
Specific gravity (SG) is a useful property in fluid mechanics and material science, representing the ratio of a substance’s density to that of water. Since water’s density at 4°C is standardized as 1 g/cm³ or 62.4 lb/ft³, specific gravity provides a quick way to estimate the density of liquids relative to water without dealing with absolute units directly.
In this problem, the specific gravity of glycerin is given as 1.258, which means glycerin is about 25.8% denser than water. When dealing with weight and volume in gallons and pounds, it’s convenient to use the density of water in pounds per gallon, which is about 8.34 lb/gal.
By multiplying the specific gravity by the density of water, we find the density of glycerin in the same units: Density of glycerin=1.258×8.34=10.49lbgal\text{Density of glycerin} = 1.258 \times 8.34 = 10.49 \frac{\text{lb}}{\text{gal}}
This means every gallon of glycerin weighs approximately 10.49 pounds.
Knowing the volume of glycerin (50 gallons), we calculate the total weight by simply multiplying volume by density: 50 gal×10.49lbgal=524.5 lb50 \, \text{gal} \times 10.49 \frac{\text{lb}}{\text{gal}} = 524.5 \, \text{lb}
This calculation is crucial in many industrial and laboratory settings where handling and transport depend on the weight of liquids, which in turn affects storage, shipping, and safety requirements.
In summary, understanding specific gravity helps convert volume measurements into weight for various liquids efficiently, avoiding the need to memorize absolute densities for every substance. Here, using specific gravity and standard water density values, we determined the weight of 50 gallons of glycerin accurately and simply.