Chapter U4, Problem 11STP

Interpretation Introduction

Interpretation:

The mass of solid potassium sulfate needs to be calculated in order to make $\text{100}\text{.0 mL}$ of $\text{0}\text{.75 M}$ solution.

Concept introduction:

The molar concentration of a solute in a solution can be expressed in terms of molarity as moles of solute present in per liter of solution. Mathematically,

$\text{Molarity = }\frac{\text{number of moles of solute}}{\text{Volume of solution (L)}}$ - (1)

Answer to Problem 11STP

The mass of solid potassium sulfate is $\text{13}\text{.0 g}$.

Explanation of Solution

Converting the given volume of sample from mL to L as:

$100\text{ mL}\times \frac{1\text{ L}}{1000\text{ mL}}=\text{ 0}\text{.1 L}$

The formula to calculate number of moles is:

$\text{number of moles = }\frac{\text{mass of the substance}}{\text{Molar mass of the substance}}$

Now, equation (1) an be rewritten as:

$\text{Molarity = }\frac{\frac{\text{mass of the solute}}{\text{Molar mass of the solute}}}{\text{Volume of solution (L)}}$ - (2)

The molar mass of potassium sulfate is $\text{174}\text{.259 g/mol}$.

Substituting the given values in equation (2) to determine the mass of solute as:

$\begin{array}{l}\text{0}\text{.75 mol/L = }\frac{\frac{\text{mass of the solute}}{\text{174}\text{.259 g/mol}}}{\text{0}\text{.1 L}}\\ \text{0}\text{.75 mol/L = }\frac{\text{mass of the solute}}{\text{0}\text{.1 L}\times \text{174}\text{.259 g/mol}}\\ \text{mass of the solute = 0}\text{.75 mol/L}\times \text{0}\text{.1 L}\times \text{174}\text{.259 g/mol}\\ \text{mass of the solute = 13}\text{.07 g}\end{array}$

Since, the mass of solid potassium sulfate is $\text{13}\text{.07 g}$ so, the correct option is (c).