Question

Determine how many grams of each of the following solutes would be needed to make $2.50\times {10}^2\mathrm{mL}$ of a $0.100-M$ solution: (a) cesium iodide (CsI), (b) sulfuric acid $\left({\mathrm{H}}_2{\mathrm{SO}}_4\right),(\mathrm{c})$ sodium carbonate $\left({\mathrm{Na}}_2{\mathrm{CO}}_3\right),$ (d) potassium dichromate $\left({\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7\right),$ (e) potassium permanganate $\left({\mathrm{KMnO}}_A\right)$

Short answer

(a) 6.495 g, (b) 2.452 g, (c) 2.650 g, (d) 7.355 g, (e) 3.951 g

Step-by-step solution

Convert Volume to Liters

The volume of the solution is given as $2.50\times {10}^2\text{ mL}$. We need to convert this to liters by using the conversion factor $1000\text{ mL}=1\text{ L}$. Thus, the volume in liters is $\frac{2.50\times {10}^2}{1000}=0.250\text{ L}$.

Calculate Moles of Solute

The concentration of the solution is given as $0.100\text{ M}$, which means $0.100\text{ moles/L}$. To find the number of moles of solute needed, use the formula: $\text{Moles of Solute}=\text{Concentration}\times \text{Volume}$. Thus, $0.100\text{ moles/L}\times 0.250\text{ L}=0.025\text{ moles of solute}$.

Calculate Mass for (a) Cesium Iodide (CsI)

First, calculate the molar mass of CsI. Molar mass of Cs (Cesium) is $132.91\text{ g/mol}$ and I (Iodine) is $126.90\text{ g/mol}$. Thus, $\text{Molar Mass of CsI}=132.91+126.90=259.81\text{ g/mol}$. Then, calculate the mass using $\text{Mass}=\text{Moles}\times \text{Molar Mass}$. So, $0.025\text{ moles}\times 259.81\text{ g/mol}=6.495\text{ g}$.

Calculate Mass for (b) Sulfuric Acid (H₂SO₄)

Calculate the molar mass of ${\mathrm{H}}_2{\mathrm{SO}}_4$. It equals $2(1.01)+32.07+4(16.00)=98.09\text{ g/mol}$. Then, the mass required is $0.025\text{ moles}\times 98.09\text{ g/mol}=2.452\text{ g}$.

Calculate Mass for (c) Sodium Carbonate (Na₂CO₃)

Calculate the molar mass of ${\mathrm{Na}}_2{\mathrm{CO}}_3$. It equals $2(22.99)+12.01+3(16.00)=105.99\text{ g/mol}$. The mass is $0.025\text{ moles}\times 105.99\text{ g/mol}=2.64975\text{ g}$.

Calculate Mass for (d) Potassium Dichromate (K₂Cr₂O₇)

Calculate the molar mass of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$. It equals $2(39.10)+2(51.9961)+7(16.00)=294.18\text{ g/mol}$. Thus, the mass needed is $0.025\text{ moles}\times 294.18\text{ g/mol}=7.3545\text{ g}$.

Calculate Mass for (e) Potassium Permanganate (KMnO₄)

Calculate the molar mass of ${\mathrm{KMnO}}_4$. It equals $39.10+54.94+4(16.00)=158.04\text{ g/mol}$. Therefore, the mass required is $0.025\text{ moles}\times 158.04\text{ g/mol}=3.951\text{ g}$.

Key concepts

Molar Mass Calculation

Molar mass is an essential concept when working with solutions. It is the mass of one mole of a given substance, typically expressed in grams per mole (g/mol). To calculate the molar mass, you sum the atomic masses of all the atoms present in the molecule. Atomic masses are usually found on the periodic table.
For instance, to find the molar mass of cesium iodide (CsI), you add the atomic mass of cesium (Cs), which is 132.91 g/mol, to that of iodine (I) which is 126.90 g/mol. The resulting molar mass is 259.81 g/mol.
This method applies to each substance in the exercise. By calculating the molar masses, you can then determine the mass needed for a specific number of moles.

Solution Preparation

When preparing a chemical solution, understanding the desired concentration and volume is critical. A solution's concentration is often expressed in molarity (M), which is the number of moles of solute per liter of solution.
To prepare a solution, you need to determine how many moles of the solute you require, based on the molarity and volume in liters. Multiply the concentration (molarity) by the volume of the solution in liters to get the total moles needed.
In the given exercise, you are asked to make a 0.100 M solution with a total volume of 250 mL, or 0.250 L. Hence, the number of moles is found by multiplying the molarity 0.100 M by the volume 0.250 L, resulting in 0.025 moles of solute.

Chemical Concentration

Chemical concentration measures how much solute is present in a given quantity of solvent or solution. Molarity is a common measure of concentration in chemistry, represented as moles per liter (mol/L).
To prepare a solution with a specific molarity, it's crucial to understand the relationship between moles, volume, and concentration. Knowing the molar mass helps convert between moles and grams, which is often necessary when physically measuring out solutes.
This exercise emphasizes the importance of calculating concentration accurately to ensure the correct mass of each solute is used to produce a solution at the desired molarity. Without precision in concentration, experiments and applications could lead to inaccurate results.

Stoichiometry

Stoichiometry is a fundamental aspect of chemistry that involves quantifying reactants and products in chemical reactions. It relies heavily on the concept of moles and balances equations to ensure the conservation of mass.
While this exercise doesn't delve into reactions, stoichiometric principles are still applied in calculating the mass of solutes needed based on their molarity and volume. Stoichiometry allows chemists to understand the proportions of substances and ensure that reactions proceed with the correct amounts of ingredients.
Though our focus here is on solution preparation, knowing how to use stoichiometry effectively aids in making precise calculations, ensuring experiments and solution preparations are both accurate and effective.