 Now let's do a question that combines some of the chemical quality concepts you just learned. So you have an 80% sulfuric acid H2SO4 concentrated solution, 80% by weight, and the rest is assumed to be manly water. Its density has been measured experimentally to be 1.73 kg per liter. Calculate the molar concentration and the molality of that solution. Ok, so let's summarize the problem. We have density equal to 1.73 kg per liter. We have the information that solution is an 80% sulfuric acid by weight. Since the question tells us to assume that the rest is water, we have the remaining 20% being water by weight, and we need the molar mass for the sulfuric acid, which we can calculate from the periodic table, which is 98.073 g per mol. Ok, so first, the molar concentration which is equal to the number of moles of sulfuric acid developed by the total volume of the solution. Now we are not given the idea of those, we are only given the density and the mass fraction, and the molar mass which comes from the identity of the compound. However, since we are only asked to calculate the molar concentration which is the same regardless of the volume, and from density we can calculate any mass or any number of moles of sulfuric acid that we want in whatever amount of volume. And since the molar concentration is the number of moles per liter, we can just set a volume to be 1 liter for convenience. So V equal to 1 liter. So now we can find the total mass of the solution when the volume is 1 liter using density. So M equal to rho density multiplied by the volume equal to 1.73 kg. So what does this mean? It means that the total mass which is the sum of the mass of the sulfuric acid and the solvent which is water is equal to 1.73 kg. So can we decompose that so that we can use the mass of the sulfuric acid to calculate the concentration? Yes we can. From the question we know that the solution is a sulfuric acid 80% by way solution. That means 80% of this total mass was 1.73 kg of sulfuric acid and 20% of that is water, presumably. So that means the mass of sulfuric acid in 1 liter of the solution is 1.73 kg multiplied 80% equal to 1.38 kg. And the mass of water in 1 liter of the solution is 1.73 kg multiplied 20% equal to 0.35 kg. So the number of moles of sulfuric acid in 1 liter of the solution is equal to the mass which we calculated above, divided by the molar mass of sulfuric acid, so that we give us 14.1 moles. And since this is the number of moles in one liter of the solution, it is therefore also the molar concentration of the solution. So C equal to N divided by V equal to 14.1 moles per liter. Before we finish, there is one more thing to do. We need to calculate the molality of the solution. So molality is the number of moles of sulfuric acid, divided by the corresponding mass of the solvent, water. And from above, in one liter of the solution we have 14.1 moles of sulfuric acid. And that solution weighs 1.73 kg, where 1.38 kg of that is sulfuric acid, 0.35 kg of that is water, which we obtained from the mass fraction. So now we can calculate the molality of the solution. And it is B equal to the number of moles of sulfuric acid, divided by the mass of water, equal to approximately 40 moles per kilogram, or 40 mol.