# What is the molality of a #"H"_2"SO"_4# solution which is #"96% w/w"# ? #M_M = "98 g/mol"#

##### 1 Answer

Here's what I got.

#### Explanation:

For starters, it's worth pointing out that the terms *solute* and *solvent* do not really apply here because sulfuric acid is **miscible** in water, meaning that the two liquids can be mixed in all proportions to form a *homogeneous mixture*, i.e. a solution.

So the classical representation of a solvent being the substance that is present in a **greater amount** does not really make sense here because sulfuric acid, which we will take as being the *solute*, is actually present in the greater amount in this solution than water, which we take as being the **solvent**.

So for the sake of simplicity, I will refer to sulfuric acid as the *solute* and to water as the *solvent*, but keep in mind that these terms are not relevant when dealing with **miscible liquids**.

As you know, **molality** is defined as the number of moles of solute present for every

This means that your first goal here will be to figure out the mass of sulfuric acid, the solute, present for every

You know that the solution is **for every** **of the solution**.

To make the calculations a little easier, let's pick a sample of this solution that has a mass of

#m_ ("H"_ 2"O") = "100 g" - "96 g"#

#m_ ("H"_ 2"O") = "4 g"#

Now, you know that you get

#10^3 color(red)(cancel(color(black)("g H"_ 2"O"))) * ("96 g H"_ 2"SO"_ 4)/(4color(red)(cancel(color(black)("g H"_ 2"O")))) = "24,000 g H"_ 2"SO"_ 4#

Next, use the **molar mass** of sulfuric acid to convert the number of grams to *moles*.

#"24,000" color(red)(cancel(color(black)("g"))) * ("1 mole H"_ 2"SO"_ 4)/(98color(red)(cancel(color(black)("g")))) = "244.9 moles H"_2"SO"_4#

Since this represents the number of moles of solute present for every **molality** of the solution is equal to

#color(darkgreen)(ul(color(black)("molality = 240 mol kg"^(-1))))#

The answer is rounded to two **sig figs**, the number of sig figs you have for the percent concentration.