Concentration Calculations
We’ve talked about qualitative ways to describe solution concentrations, and you’re familiar with words like “dilute”, but today we are going to express concentrations of solutions quantitatively. There are a few different ways that this is commonly done.
The concentrations of many liquid solutions in your house are expressed as Percent by Volume:
Look at this bottle of vinegar, for example; it says 5% acidity. Knowing that the rest of it is water, and the total volume of the bottle is 250ml, we can figure out what the actual volume of acetic acid is here:
Another way of expressing concentrations that we’ve talked about before is Percent by Mass:
A third way of expressing concentrations is in Parts per Million (ppm). This method is useful to report concentrations that are too dilute to use other methods.
Maximum allowable contaminants are usually reported in ppm. For example, the EPA allows 4ppm of chlorine in drinking water.
Example) The FDA says that the maximum amount of mercury allowed in fish to be sold for human consumption is 1ppm. If a 50kg tuna is at that level, how many grams of mercury does it contain?
Molarity, M, of a solution is the number of moles of solute contained in 1 liter of solution.
In other words:
A 3 M solution = 3 moles of solute per liter of solution, or
A 0.5 M solution = 0.5 moles of solute per liter of solution
To solve molarity problems you always need to have moles and liters!
Sample Problems
1) What is the molarity of a solution that contains 4 moles of solute in 8L of solution?
2) What is the molarity of a solution that contains 170 grams of sodium nitrate (NaNO3) in 2 liters of solution?
3) How many grams of hydrogen chloride (HCl) are present in 5.0 liters of a 6M solution of hydrochloric acid?
4) What is the molarity of a solution that contains 4 grams of NaOH in 500 milliliters of solution?
Let’s try some example problems now:
1. A swimming pool reading reports that chlorine is present at 30 ppm. How many grams of chlorine are present in 1000 grams of pool water?
2. What is the percent by mass of a solution if 60 g of HCl is added to 90g of water?
3. Carbon dioxide gas has a solubility of 0.0973 grams per 100 grams of water at 40°C. What is this in ppm?
4. A 250 ml sample of air at STP contains approx. 52.5 ml of oxygen gas. What is the percent of oxygen by volume in air?