Specific Gravity - Online Tutor, Practice Problems & Exam Prep

Specific Gravity

Now, if you've heard about density, you might have heard about specific gravity. Specific gravity represents the density of a substance divided by the density of water at the same temperature. Since the units cancel out when it comes to specific gravity, we're going to say that it is unitless. So specific gravity has no units involved. As the temperature changes, the density of water changes. If we take a look here, we have the specific gravity of water, and again that's the density of a substance in grams per milliliter if we're assuming it's in liquid or solid form, divided by the density of water. The units would cancel out, and that's why specific gravity is unitless. We just said that as the temperature changes, the density of water changes. We tend to see here that the density of water is 1.0 grams per milliliter. That is not exactly true. That's only true when the temperature is exactly 3.98 degrees Celsius. If the temperature were to change, the density of water slightly changes. We can see here the density of water at negative 30 degrees Celsius, 0 degrees Celsius, 10 degrees Celsius, 25 degrees Celsius, and 100 degrees Celsius. We see that the density is slightly changing as we increase the temperature. The general trend is that it is decreasing as we go higher and higher in terms of temperature. So just remember, specific gravity is the density of a substance divided by the density of water. Units cancel out means that specific gravity has no units.

Specific Gravity Example 1

Here we're told that if the specific gravity of sulfuric acid is 1.27 at room temperature, which is 25 degrees Celsius, what is its mass in milligrams for 2.3 liters? Alright. So remember, specific gravity equals the density of the substance, which is sulfuric acid, divided by the density of water. So let's fill in the parts that they're telling us. They tell us that the specific gravity of sulfuric acid is 1.27. With the temperature, we can look at the chart and see what the density of water at 25 degrees Celsius is. That would be 0.99700 grams per milliliter. And here, this will be our x. We don't know what the density of sulfuric acid is. Alright. So what we're gonna do first is we're gonna cross multiply these 2 together, so 1.27 times the density of water at 25 degrees Celsius. When we do that, that's going to give me x=1.26619 grams per milliliter. Okay? That's gonna be grams per 1 milliliter. Now they're giving us 2.3 liters. Here, if we convert that to milliliters, that comes out to 2300 milliliters. And what we need to realize here is that now if I bring in the 2300 milliliters here, they will cancel out with the milliliters from the density we isolated, and that would give me the mass of sulfuric acid at this point, which would come out to 2912.237 grams. But remember, they're not asking for the answer in grams, they want it in milligrams. So we have to do one more conversion. Grams go on the bottom, milligrams go on top. Remember, milli, the metric prefix is 10^-3. Milligrams cancel out and now we're gonna have milligrams as our answer, which is gonna come out to 2.9×10⁶ milligrams when you convert it into scientific notation. Here, we have our answer as 2.9, which has 2 significant figures because 2.3 has 2 significant figures, this has 3 significant figures, this has 2 significant figures. Remember, we go with the least number of significant figures. So, again, our answer here would be 2.9×10⁶ milligrams for 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

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