To determine the molarity of a sulfuric acid solution that is 5% sulfuric acid with a density of 0.9918 grams per milliliter, we start by understanding the concept of molarity, which is defined as the number of moles of solute per liter of solution.
Given that the solution is 5% sulfuric acid, this means there are 5 grams of sulfuric acid in every 100 grams of solution. To convert grams of sulfuric acid to moles, we use the molar mass of sulfuric acid (H2SO4), which is approximately 98.086 grams per mole. Thus, we can calculate the moles of sulfuric acid:
\[\text{Moles of } H_2SO_4 = \frac{5 \text{ grams}}{98.086 \text{ grams/mole}} \approx 0.0510 \text{ moles}\]
Next, we need to convert the mass of the solution to volume using the density. The density of the solution is 0.9918 grams per milliliter, which allows us to find the volume of 100 grams of solution:
\[\text{Volume} = \frac{100 \text{ grams}}{0.9918 \text{ grams/mL}} \approx 100.83 \text{ mL}\]
To convert milliliters to liters, we use the conversion factor that 1 mL is equal to \(10^{-3}\) L:
\[\text{Volume in liters} = 100.83 \text{ mL} \times 10^{-3} \text{ L/mL} \approx 0.10083 \text{ L}\]
Now, we can calculate the molarity (M) of the sulfuric acid solution by dividing the moles of sulfuric acid by the volume of the solution in liters:
\[\text{Molarity} = \frac{0.0510 \text{ moles}}{0.10083 \text{ L}} \approx 0.5056 \text{ M}\]
Finally, rounding to two significant figures, the molarity of the sulfuric acid solution is approximately 0.51 M. This calculation illustrates the process of converting mass percent to molarity using molar mass and density, essential for understanding solution concentrations in chemistry.