Specific Gravity: Videos & Practice Problems

Specific gravity is defined as the density of a substance divided by the density of water at the same temperature, making it a unitless measure. The density of water is approximately 1.0 g/mL at 3.98°C, but it varies with temperature, generally decreasing as temperature increases. Understanding specific gravity is essential in fields like chemistry and physics, as it relates to concepts such as density, buoyancy, and material properties.

Specific Gravity

Specific gravity is a crucial concept in understanding the relationship between the density of a substance and the density of water. It is defined as the ratio of the density of a substance to the density of water at the same temperature. Since the units of density (grams per milliliter) cancel out in this ratio, specific gravity is considered a unitless quantity.

It's important to note that the density of water is not a constant value; it varies with temperature. The commonly accepted density of water is 1.0 grams per milliliter, but this is only accurate at approximately 3.98 degrees Celsius. As the temperature changes, the density of water also changes slightly. For instance, at temperatures such as -30 degrees Celsius, 0 degrees Celsius, 10 degrees Celsius, 25 degrees Celsius, and 100 degrees Celsius, the density of water decreases as the temperature increases. This trend highlights the importance of temperature in calculations involving specific gravity.

In summary, specific gravity serves as a useful tool in comparing the density of various substances to that of water, emphasizing that it is a dimensionless quantity influenced by temperature variations in water's density.

Specific Gravity Example 1

To determine the mass of sulfuric acid in milligrams for a volume of 2.3 liters, we start by using the concept of specific gravity. Specific gravity is defined as the ratio of the density of a substance to the density of water. In this case, the specific gravity of sulfuric acid is given as 1.27 at 25 degrees Celsius.

First, we need to find the density of water at this temperature, which is approximately 0.997 grams per milliliter. Using the formula for specific gravity:

$\mathrm{SG}=DD$

where SG is specific gravity, D is the density of sulfuric acid, and D_w is the density of water. We can rearrange this to find the density of sulfuric acid:

$D=\mathrm{SG}\times D$_w

Substituting the known values:

$D=\; 1.27\; \times \; 0.997\; \backslash text\{\; g/mL\}$

This calculation yields a density of approximately 1.266 g/mL for sulfuric acid.

Next, we convert the volume of sulfuric acid from liters to milliliters:

2.3 liters = 2300 milliliters.

Now, we can calculate the mass of sulfuric acid using the formula:

$\mathrm{mass}=\mathrm{density}\times \mathrm{volume}$

Substituting the values we have:

$\mathrm{mass}=\; 1.266\; \backslash text\{\; g/mL\}\; \times \; 2300\; \backslash text\{\; mL\}$

This results in a mass of approximately 2912.237 grams. Since the problem requests the mass in milligrams, we convert grams to milligrams:

1 gram = 1000 milligrams, so:

$\mathrm{mass}=\; 2912.237\; \backslash text\{\; g\}\; \times \; 1000\; \backslash text\{\; mg/g\}\; =\; 2.912237\; \backslash times\; 10^6\; \backslash text\{\; mg\}$

Rounding to the appropriate number of significant figures, based on the least precise measurement (2.3 liters has 2 significant figures), the final answer is:

2.9 × 10⁶ milligrams of sulfuric acid.

What is the specific gravity of lithium metal (in g/mL) at 10.0ºC if a cube measures 0.82 cm x 1.45 cm x 1.25 cm and has a mass of 0.794 g?

• A. 0.55
• B. 0.504
• C. 0.53
• D. 1.87

Answer: (C)

Ethyl alcohol has a specific gravity of 0.7892 at 10ºC. What is the volume of 250 g of ethyl alcohol?

• A. 317 mL
• B. 197 mL
• C. 320 mL
• D. 371 mL

Answer: (C)

Here’s what students ask on this topic:

What is specific gravity and how is it calculated?

Specific gravity is a unitless measure that compares the density of a substance to the density of water at the same temperature. It is calculated using the formula:

$\frac{\rho \left(\mathrm{substance}\right)}{\rho \left(\mathrm{water}\right)}$

where $\rho \left(\mathrm{substance}\right)$ is the density of the substance and $\rho \left(\mathrm{water}\right)$ is the density of water. Since the units cancel out, specific gravity is dimensionless.

Why is specific gravity considered unitless?

Specific gravity is considered unitless because it is the ratio of the density of a substance to the density of water at the same temperature. When you divide the density of the substance (in units like g/mL) by the density of water (also in g/mL), the units cancel out. This leaves a pure number without any units, making specific gravity a dimensionless quantity.

How does temperature affect the specific gravity of water?

Temperature affects the specific gravity of water because the density of water changes with temperature. At 3.98°C, the density of water is approximately 1.0 g/mL. As the temperature increases or decreases from this point, the density of water changes slightly. Generally, the density of water decreases as the temperature increases, which in turn affects the specific gravity calculations for other substances when compared to water at different temperatures.

What is the significance of specific gravity in scientific fields?

Specific gravity is significant in various scientific fields such as chemistry, physics, and engineering. It helps in identifying substances, determining material properties, and understanding buoyancy. For example, in chemistry, specific gravity can help identify unknown substances by comparing their densities to water. In engineering, it is used to design systems involving fluids, ensuring materials will float or sink as required. Understanding specific gravity is crucial for accurate measurements and applications in these fields.

How does specific gravity relate to buoyancy?

Specific gravity is directly related to buoyancy, which is the ability of an object to float in a fluid. If the specific gravity of a substance is less than 1, it will float in water because its density is less than that of water. Conversely, if the specific gravity is greater than 1, the substance will sink. This principle is used in designing ships, submarines, and other floating structures, ensuring they remain buoyant in water.