Working Through the Density of Pennies Lab
Most students hit a wall when they try to actually complete the density of pennies lab. The procedure is simple on paper. Measuring mass and volume, plugging into the formula, getting a number. The problem comes in the execution, and that's where the answer key becomes useful rather than just a shortcut. Before I get into what you actually need from an answer key, here's what the lab looks like in practice. You take pre-1982 pennies and post-1982 pennies. Pre-82 are mostly copper, post-82 are zinc with a copper plating. That year split matters because the density shifts from about 8.8 g/cm³ down to roughly 7.0 g/cm³. Your answer key should reflect that difference, not just give one number. The actual experiment goes like this. Measure out a stack of ten pennies. Record the mass. Then add them to a graduated cylinder with water and record the volume displacement. Repeat with stacks of twenty, thirty, forty, fifty. Plot mass versus volume. The slope of your line is the density. A proper answer key shows the expected slope values, but more importantly it shows what your data should look like if everything went right.
I ran this lab with a class last spring and half the groups got densities around 5 or 6 for their post-82 pennies. Turned out they were using 25 mL of water to start and reading the meniscus wrong. The displacement was so small relative to their starting volume that the reading error ate up most of their data. The fix was switching to 50 mL as the baseline and having them read at eye level. Their numbers jumped to the correct range immediately. A solid answer key will include the accepted values so you can check your work. For pre-1982 pennies you're looking at 8.83 g/cm³. For post-1982 it's closer to 7.14 g/cm³. If your calculated density for pre-82 pennies is coming out below 8.0, something went wrong with your measurements. More likely it's a volume reading issue than a mass issue because balances are usually reliable. Here's something most student answer keys won't tell you. The copper plating on post-1982 pennies affects your measurement slightly. If you're getting a density between 7.5 and 8.0 for post-82 pennies instead of right at 7.14, don't automatically assume error. The plating adds a small amount of copper mass without adding much volume. It's a real effect, not a mistake. Some teachers mark this down though, so know the difference between experimental artifact and actual procedural error.
Another thing that trips people up is the water absorption issue. Old pennies, especially pre-82 ones sitting around in a jar, can have slight surface oxidation. That doesn't change the mass significantly but it does affect volume if water gets trapped in the patina. Not a huge deal with ten pennies but it shows up as scatter in your data points. Tossing the pennies in distilled water and drying them before each trial reduces this variability. If you're looking for an answer key to check your results, here's what to verify it contains. Expected mass values for each stack size. Expected volume readings. The calculated slope from a linear regression, not just an average of individual densities. And notes about the 1982 transition year being messy because some 1982 pennies are copper and some are zinc. That detail alone will cost you points if you ignore it. The best answer keys also flag common mistakes. Using the wrong graduated cylinder size. Counting pennies incorrectly. Forgetting to subtract the initial water volume. These seem obvious until you're grading thirty labs and half the errors are the same three things repeated.
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One more practical note. Some schools use the penny lab to teach linear regression properly. The answer key should show the equation of the line, not just a final density number. R-squared values matter too. If your R² is below 0.95, your data collection has problems regardless of how close your slope is to the accepted value. That's usually the part students miss when they just compare their answer to the key and move on. Download resources for this lab tend to vary in quality. The ones from university education departments or state science standards sites are usually the most reliable. Avoid random worksheet sites that only list a single density number without context. A good answer key explains the method, shows sample data, and notes the limitations. Anything less is probably just copied from somewhere without someone actually running the experiment.
