The cost on the shipping of chemicals is dependent upon the weight of cargo upon loading. You have a choice of purchasing 9,000 gallons of ethanol from Florida or Minnesota. The temperature of the cargo leaving Minnesota is 15.0oC while the temperature of the cargo leaving Florida is 30.5oC. How many pounds are you buying from Minnesota?
To determine the weight of the cargo in pounds, we need to use the specific gravity of ethanol and the volume (in gallons) of ethanol being purchased.
First, let's find the specific gravity of ethanol at the given temperatures of 15.0oC and 30.5oC. The specific gravity of a substance is the ratio of its density to the density of a reference substance. In this case, we'll use water as the reference substance.
The specific gravity of ethanol at 15.0oC is 0.789, and at 30.5oC is 0.776.
Next, we need to convert the volume of ethanol from gallons to liters, as the specific gravity is typically given in relation to liters. One gallon is approximately equal to 3.78541 liters.
So, for the volume in gallons:
Volume in liters from Minnesota = 9,000 gallons × 3.78541 liters/gallon
Now, we can calculate the weight in pounds using the specific gravity and the volume in liters:
Weight in pounds from Minnesota = Volume in liters from Minnesota × Specific gravity at 15.0oC
You can use the same approach to calculate the weight in pounds for ethanol from Florida using the specific gravity at 30.5oC.
Let's substitute the values and calculate the weight in pounds from Minnesota.
Look up the density of ethanol at 15.0oC and 30.5oC. It would make it easier if you found it in lbs/gallon but if not than you must convert. Then
mass = volume x density.