How many grams of sodium chloride, NaCl, must be added to make 100 milliliters of 0.5 molar NaCl? A) 1.4 grams, B) 2.9 grams, C) 7.0 grams, D) 15 grams, or E) 58.5 grams.
The practical set-up we might be looking at here starts with 100-milliliter volumetric flask. And then, what we might do is measure out a specific mass of sodium chloride on a balance. And then transfer the solid into the volumetric flask, perhaps using a solid addition funnel. In the next step, we’d add water and probably rinse down the neck to make sure any solid stuck to the sides is pushed to the bottom. We let the salt dissolve. And then, we top it up, perhaps using a pipette, towards the end to make sure that the meniscus exactly sits on the graduation. This way, we’d end up with 100 mil of a solution measured very accurately. What we have to figure out is what mass of sodium chloride we would have had to add, in the first place, to produce a solution with a concentration of 0.5 molar.
Well, we have to start with the concentration we’re given, which is 0.5 moles of NaCl per one liter. The unit molars is equivalent to moles per liter. But we’re only making 100 milliliters of solution, not a liter. So we need to convert our liters to milliliters. 1000 milliliters is equivalent to a liter. So we can convert to milliliters by multiplying by one liter per 1000 milliliters. This gives us concentration of 0.0005 moles of NaCl per milliliter. We can then multiply by our volume, 100 milliliters, to put our expression in terms of moles of NaCl. This gives us 0.05 moles of NaCl. The last thing to do is convert this into a mass. To do this, we’ll need the molar mass of NaCl. The atomic mass of sodium is 23 unified atomic mass units. So sodium contributes one times 23 grams per mole to a molar mass. The atomic mass of chlorine is 35.5 unified atomic mass units. So chlorine, in this case, contributes 35.5 grams per mole to a molar mass.
When we sum these two together, we get the molar mass of sodium chloride to be 58.5 grams per mole of sodium chloride. So in the last step, we convert from moles of sodium chloride into mass of sodium chloride by multiplying by 58.5 grams per mole. So our final expression is 0.5 times 58.5 grams divided by 10. We can do the mental math in stages. Let’s start by multiplying by 0.5, which is the same as dividing by two. 58.5 divided by two is 29.25 grams. And when we divide that by 10, we get 2.925 grams, which is 2.9 grams to two significant figures. Meaning that the number of grams of sodium chloride in 100 milliliters of 0.5 molar sodium chloride is 2.9 grams.