Determine the molarity of a sulfuric acid solution. That is 5% sulfuric acid with a density of 0.9918 grams per milliliter. All right, so remember, molarity itself is capital M, so we need to isolate the units of moles over liters in order to isolate molarity. All right, So remember that when we are given a mass percent, it can be used as a conversion factor as well, so 5%. So sulfuric acid here really means 5 grams of sulfuric acid per 100 grams of solution.
And here we have the density of the solution, which is 0.9918 grams of solution per one milliliter of solution. All right, so how do we use this information to help us get to our molarity? All right. So we're going to start out with our mass percent, which is 5.0 grams of sulfuric acid per 100 grams of solution. All right? And we're going to say here, we want to get rid of the grams of sulfuric acid and isolate moles of sulfuric acid. So for everyone mole of sulfuric acid the molar mass of it is 98.086 grams. Grams here cancel out.
Now I have moles of sulfuric acid over grams of solution. Next I need to get rid of grams of solution because remember molarity has liters on the bottom. We do this by using our density. So here our density is 0.9918 grams of solution per one milliliter of solution. So here grams of solution cancel out and now I have milliliters of solution. I'm almost there. All I got to do now is just change these milliliters into liters. So remember that one milli is equal to 10-3 liters and like that we've isolated moles over liters.
So we've just isolated our molarity. So when we plug that in, we're going to get 0.5056 molar. Now since this has two sig figs, we'll just bring this down at two sig figs as well. So this is 51 molar. So that'll be our molarity for this given solution of sulfuric acid.