# Question Video: Calculating Paracetamol Concentration Chemistry

A 500 mg tablet of paracetamol (C₈H₉NO₂) was dissolved in 200 mL of water. What is the concentration of the resulting solution? Give your answer in units of mol/dm³ and to 2 significant figures.

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### Video Transcript

A 500-milligram tablet of paracetamol, C8H9NO2, was dissolved in 200 milliliters of water. What is the concentration of the resulting solution? Give your answer in units of moles per decimeter cubed and to two significant figures.

This question is asking us to work out the concentration of a solution. In order to do this, we’re going to need a key equation. Of course, the equation we need is 𝑛 equals 𝑐𝑣, where 𝑛 is the number of moles, 𝑐 is the concentration, and 𝑣 is the volume. We’re given the value of 𝑣, volume, in the question as 200 milliliters. However, the question specifically asks for our answer in units of moles per decimeter cubed. So we’re going to need to do some unit conversion. Remember that decimeters cubed are exactly the same as liters. So you can imagine giving our answer in units of moles per liter.

But the volume we’re given is in milliliters. So we’re going to need to convert our milliliters into liters. To convert milliliters to liters, we need to multiply by one liter per 1000 milliliters. You can remember that there are 1000 milliliters per liter by remembering that the prefix milli- means thousandth. Performing this conversion gives us 0.2 liters. As a side note, remember that milliliters are exactly the same as centimeters cubed. Now that we have our volume in the right units and we know that we’re working out the concentration, we just need to find the number of moles, 𝑛.

However, in the question, we’re not given the number of moles. Instead, we’re given a mass in milligrams. So we’re going to need to convert our mass into the number of moles. To do this, we need another key equation. The equation we need is moles equals the mass divided by molar mass, where our units are moles, grams, and grams per mole. So the first thing we need to do is convert our mass from milligrams into grams. Converting from milligrams to grams is very similar to converting milliliters to liters in that we multiply by one gram divided by 1000 milligrams. So converting 500 milligrams into grams, we multiply by one gram per 1000 milligrams, leaving us with 0.5 grams.

Now we can begin to work out the number of moles. From our second key equation, we know that the number of moles equals 0.5 grams divided by the molar mass of paracetamol. To work out our molar mass, we need the periodic table and the formula for paracetamol given in the question. We can see that it contains eight carbon atoms, nine hydrogen atoms, one nitrogen atom, and two oxygen atoms. So to get our molar mass, we add the masses of eight carbons, nine hydrogens, one nitrogen, and two oxygens altogether, which gives us a molar mass of 151.165 grams per mole.

We can now use this to work out the number of moles of our paracetamol. So 𝑛 equals 0.5 grams divided by 151.165 grams per mole, which gives us 0.0033076 moles. Now that we have both 𝑛 and 𝑣, we can use 𝑛 equals 𝑐𝑣 to give us the concentration. Rearranging our equation in terms of 𝑐, we get 𝑐 equals 𝑛 divided by 𝑣. By inputting our values, we get concentration equals 0.0033076 moles divided by 0.2 liters. This works out at 0.016538 moles per liter.

However, we’re not finished yet. The question asks for our answer to be given to two significant figures and with units of moles per decimeter cubed. Rounding to two significant figures gives us 0.017. And since liters are the same as decimeters cubed, we don’t need to do anything regarding units. We can simply write the units as moles per decimeter cubed. And this is our final answer.