Question

What mass of iron(III) chloride is needed to prepare 1.00 \(\mathrm{L}\) of a 0.255 \(\mathrm{M}\) solution? (Chapter 14\()\)

Short answer

To prepare 1.00 L of a 0.255 M solution of iron(III) chloride (FeCl₃), 41.36 g of iron(III) chloride is needed.

Step-by-step solution

Find the moles of solute needed

Given the molarity (M) and the volume (V) of the solution, we can calculate the moles of solute (n) needed using the formula: Moles of solute needed (n) = Molarity (M) × Volume (V) The given molarity is 0.255 M, and the volume is 1.00 L. Plugging these values into the formula, we get: n = 0.255 M × 1.00 L n = 0.255 mol So, we need 0.255 moles of FeCl₃ to prepare the solution.

Find the molar mass of iron(III) chloride (FeCl₃)

To calculate the mass of FeCl₃ needed, we first need the molar mass of FeCl₃. This can be calculated using the atomic masses of the elements (Fe and Cl) found in the periodic table. Iron (Fe) has an atomic mass of 55.85 g/mol, and chlorine (Cl) has an atomic mass of 35.45 g/mol. Molar mass of FeCl₃ = atomic mass of Fe + 3 × atomic mass of Cl Molar mass of FeCl₃ = 55.85 g/mol + 3 × 35.45 g/mol Molar mass of FeCl₃ = 55.85 g/mol + 106.35 g/mol Molar mass of FeCl₃ = 162.20 g/mol

Calculate the mass of FeCl₃ needed

Now that we know the moles of FeCl₃ needed and its molar mass, we can find the mass required by using this formula: Mass (g) = moles × molar mass Plugging in the values we found in the previous steps: Mass (g) = 0.255 mol × 162.20 g/mol Mass (g) = 41.36 g So, 41.36 g of iron(III) chloride is needed to prepare 1.00 L of a 0.255 M solution.

Key concepts

Moles of Solute

Understanding the concept of moles of solute is crucial when preparing solutions in chemistry. The "mole" is a unit that chemists use to measure the amount of a substance. One mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\) particles. This could be atoms, molecules, ions, etc.
Moles help determine how much of a substance is involved in a reaction or required to create a certain concentration in a solution. For instance, to find out how many moles of a substance you need in a solution, use the formula:

• Moles of solute (n) = Molarity (M) × Volume (V)

Using this formula lets you calculate the right amount of solute needed to achieve the desired concentration.

Molar Mass

Molar mass is a key concept in chemical calculations. It refers to the mass of one mole of a compound, measured in grams per mole (g/mol). Knowing the molar mass of a compound allows you to convert between grams and moles, which is often necessary when preparing solutions.
Calculating the molar mass involves adding up the atomic masses of all the atoms in a molecule. For example, the molar mass of iron(III) chloride \( \text{FeCl}_3 \) is calculated as follows:

• Atomic mass of Fe = 55.85 g/mol
• Atomic mass of Cl = 35.45 g/mol
• Molar mass of \( \text{FeCl}_3 \) = 55.85 g/mol + 3 × 35.45 g/mol = 162.20 g/mol

This knowledge is essential for determining how much of a compound you have or need.

Molarity

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution, represented by the unit \( \,\text{M} \) (moles per liter). Molarity allows chemists to easily communicate and reproduce solution concentrations.
When preparing a solution with a specific molarity, calculate the moles of solute needed by multiplying the desired molarity by the volume of the solution. For example, to make a 1.00 L solution with a molarity of 0.255 M, you would need:

• Moles of solute \( = 0.255 \,\text{M} \times 1.00 \,\text{L} = 0.255 \,\text{mol} \)

Molarity is crucial for ensuring that solutions have the proper concentration for reactions.

Iron(III) Chloride

Iron(III) chloride, with the chemical formula \( \text{FeCl}_3 \), is a compound composed of iron and chlorine. It is used in various applications such as water treatment and as a catalyst in organic synthesis. Understanding its properties, such as molar mass, is vital when working with this compound.
To use iron(III) chloride effectively in a laboratory setting, one must calculate the correct amounts required for solutions. This involves knowing both its molar mass and the molarity needed for the solution.
With the molar mass of iron(III) chloride being 162.20 g/mol, calculate the grams required by multiplying this by the moles needed, based on the solution's molarity and volume.

Chemical Calculations

Chemical calculations are fundamental for accurate science and lab work. They encompass a variety of mathematical computations used in chemistry to quantify substances, reactions, and solutions.
For instance, determining how much iron(III) chloride to use in a solution involves several key calculations:

• Calculate moles using molarity and volume: \( n = M \times V \)
• Then calculate mass using molar mass: \( \text{Mass} = n \times \text{Molar Mass} \)

These chemical calculations ensure you mix substances in the right proportions, crucial for the success of many experiments and reactions. With these tools, chemists can predict and control the outcomes of chemical processes effectively.