2. Tools of the Trade
Buoyancy
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So here it says the density of propane and odorless hydrocarbon compound used in cooking is 0.922 grams per milliliter. Weire asked when a sample of it is placed on an analytical balance, a weight of 8.15 times 10 to the 8 a weight of 8.15 times 10 to the 8 nanograms is obtained. Calculate the true mass of propane. All right, so we're looking for the true mass. That means we're looking for the mass of an analyte when we're weighing it on an analytical balance. Now we're going to going to have to use the buoyancy equation. So that is mass true mass of my object is equal to the mass of it when it's on the analytical balance times 1 minus the density of air divided by the density of water. And then on the bottom, we have 1 minus the density of air divided by the density of the object or analyte itself. Now, we need to have the mass of the analyte in grams. It's given to us here in nanograms. So, just remember we have 8.15 times 10 to the 8 nanograms. For every 1 nanogram, it's 10 to the negative 9 grams. So that means that the weight according to the analytical balance is 8.15 times 10 to the negative one grams. We're going to have 1 minus the density of air which is 0.0012 grams per milliliter divided by the density of water, and here would be 8.0 grams per milliliter. Then on the bottom, we're going to divide by 1 minuteus the density of air again. And then it's going to be our, the density of the object itself. So here that would be 0.922 grams per milliliter like what we're told right here. So, when I do 1 minuteus the density of air divided by the density of water, I'm going to get here, 0.999 85. The density units cancel out. Then, we're going to divide by 1 minuteus the density of air divided by the density of the object itself gives me 0.998698. Now here, we're going to want our answer to have 3 significant figures because 8.15 has 3 significant figures in it. When we do that, we get 0.81 594 grams which at the end gives us 0.816 grams as the true mass of my object once I've taken into account airflow. Now finally, take a look at the final practice example that's left at the bottom of the page. Attempt to do it on your own. But again, as always, if you get stuck, don't worry. Just come back and take a look at how I approach on answering that practice question.
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