# Video: Estimating the Density of Propanol Given the Mass of a Given Volume of Propanol and Its Container, and the Mass of the Same Volume of Water and Its Container, Given the Density of Water

A 10 mL container filled with water had a mass of 39 g at 4°C. The same container containing propanol had a mass of 37 g. What is the approximate density of propanol? (The density of water at 4°C is 1.00 g/mL) [A] 0.80 g/mL [B] 1.0 g/mL [C] 1.3 g/mL [D] 2.1 g/mL [E] 3.3 g/mL

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### Video Transcript

A 10-milliliter container filled with water had a mass of 39 grams at four degrees Celsius. The same container containing propanol had a mass of 37 grams. What is the approximate density of propanol? The density of water at four degrees Celsius is 1.00 grams per milliliter. A) 0.80 grams per milliliter, B) 1.0 grams per milliliter, C) 1.3 grams per milliliter, D) 2.1 grams per milliliter, or E) 3.3 grams per milliliter.

This question is asking us to find the density of propanol, which is the mass of propanol divided by the volume of propanol. The problem tells us that the propanol fills a 10-milliliter container. So the volume of propanol is 10 milliliters. But the mass that we’re given for propanol is not just the mass of propanol. It’s the mass of the container plus the mass of the propanol inside the container.

So in order to find the density of propanol, we’re first going to need to find the mass of propanol. And to do that, we’ll need to find the mass of the container. We’re told that the same container when it’s filled with water weighs 39 grams. The water is in the same 10-milliliter container. So we know the volume of the water. And we’re given the density of the water.

So given the information in the problem, we should be able to first find the mass of the water and then use that to find the mass of the container. And then find the mass of propanol, which we can then finally use to solve for the density of propanol.

First, let’s find the mass of the water. We can do this by rearranging the formula for density of the water. If we multiply both sides by the volume, we’ll find that the mass of the water will be equal to the density of the water times the volume of the water. The density of the water is 1.0 grams per milliliter. And the volume of water is 10 milliliters. So the water has a mass of 10 grams.

We know that, together, the mass of the container and the mass of water equals 39 grams. So we can find the mass of the container by subtracting the mass of water over to the other side. We just found that the mass of water is 10 grams. So 39 grams minus 10 grams gives us 29 grams for the mass of the container.

Now we can find the mass of just the propanol by subtracting the mass of the container that we just found from the mass of the container and the propanol together. This gives us eight grams for the mass of propanol.

Now we can finally solve for the density of the propanol by dividing the mass of the propanol by the volume of the propanol. We just found that the mass of the propanol is eight grams. And the volume of the propanol is 10 milliliters. This gives us 0.8 grams per milliliter for the density of propanol, which matches answer choice A.

We know that this answer makes sense because the mass of the propanol was less than the mass of water. But they were in the same volume of container. So the density of propanol should be smaller than the density of water.