Specific Gravity of Alcohol and Its Calculation: A Detailed Guide

Understanding the specific gravity of a substance, such as alcohol, is crucial in many scientific and industrial applications. This article will guide you through the process of calculating the specific gravity of alcohol when a block of mass is submerged in it. We will use a real-world example to illustrate how to derive the specific gravity step-by-step, ensuring clarity and accuracy in the process.

Introduction to Specific Gravity and Buoyancy

The specific gravity of a substance is the ratio of its density to the density of a reference substance. In this context, we will be dealing with the specific gravity of alcohol relative to water. Specific gravity can also be understood as a measure of the buoyancy of an object in a fluid or the density of the substance relative to another reference substance, typically water.

Understanding the Problem

In a specific scenario, a block of mass is given. The mass of the block in air is 105.1 grams, while the mass of the block when completely submerged in alcohol is 74.5 grams. The volume of the displaced alcohol, which is equal to the volume of the block, is 3.90×10-5 m3.

Calculating the Bouyancy Force

First, we need to calculate the bouyancy force. The bouyancy force is the upward force exerted by a fluid on an object submerged in it, and it is equal to the weight of the fluid displaced by the object.

The formula to calculate the bouyancy force is:

[ W_B W_{A} - W_{W} ]

Where:

- ( W_B ) is the bouyancy force or weight of the displaced alcohol - ( W_A ) is the weight of the solid in the liquid (alcohol) - ( W_W ) is the weight of the solid in air

Substituting the given values:

[ W_B 105.1 text{ g} - 74.5 text{ g} 30.6 text{ g} ]

This means the weight of the displaced alcohol is 30.6 grams.

Finding the Density of Alcohol

The density of a substance is given by the mass of the substance divided by its volume. Here, we need to find the density of the alcohol. The formula for density is:

[ rho frac{m}{V} ]

Where:

- ( rho ) is the density of the alcohol in g/cm3 - ( m ) is the mass of the alcohol (30.6 grams) - ( V ) is the volume of the displaced alcohol (3.90×10-5 m3)

First, we convert the volume from cubic meters to cubic centimeters:

[ 3.90 times 10^{-5} text{ m}^3 3.90 times 10^{-5} times 10^6 text{ cm}^3 0.039 text{ cm}^3 ]

Now, we can calculate the density:

[ rho frac{30.6 text{ g}}{0.039 text{ cm}^3} 0.7846 text{ g/cm}^3 ]

Determining the Specific Gravity

Specific gravity is the ratio of the density of the alcohol to the density of water. The density of water is generally taken as 1 g/cm3. Therefore, the specific gravity ( SG ) of alcohol is:

[ SG frac{rho_{text{alcohol}}}{rho_{text{water}}} frac{0.7846 text{ g/cm}^3}{1 text{ g/cm}^3} 0.7846 ]

Rounded to three significant figures, the specific gravity of the alcohol is approximately 0.785.

Conclusion

The specific gravity of alcohol, as calculated from the mass and volume of a displaced alcohol block, is 0.785. This value is crucial for applications such as determining the purity of alcohol, designing fluid systems, and understanding the behavior of objects in different liquids.

References

1. Specific Gravity Calculation Tutorial 2. Density Calculator