Question

Calculate the mass of KI in grams required to prepare \(5.00 \times 10^{2} \mathrm{~mL}\) of a \(2.80-M\) solution.

Short answer

232.40 g of KI is needed.

Step-by-step solution

Understanding the problem

We need to find out how many grams of KI (potassium iodide) are needed to make a 500.0 mL solution with a molarity (M) of 2.80 mol/L. Molarity (M) is defined as moles of solute per liter of solution.

Calculate moles of KI

First, convert the volume from mL to liters by dividing by 1000: \(500.0 \, \text{mL} = 0.500 \, \text{L}\). Next, use the molarity formula to calculate the moles of KI needed: \(\text{Moles of KI} = \text{Molarity} \times \text{Volume in L} = 2.80 \, \text{mol/L} \times 0.500 \, \text{L} = 1.40 \, \text{mol}\).

Determine molar mass of KI

To convert moles to grams, we need the molar mass of KI. Potassium (K) has a molar mass of approximately 39.10 g/mol, and iodine (I) has a molar mass of approximately 126.90 g/mol. Therefore, the molar mass of KI is:\(39.10 \, \text{g/mol} + 126.90 \, \text{g/mol} = 166.00 \, \text{g/mol}\).

Calculate mass of KI

Use the formula \(\text{Mass} = \text{Moles} \times \text{Molar Mass}\) to calculate the mass:\(1.40 \, \text{mol} \times 166.00 \, \text{g/mol} = 232.40 \, \text{g}\).

Final answer

Therefore, you need 232.40 grams of KI to prepare the desired solution.

Key concepts

Molarity Calculation

Molarity is a way to express the concentration of a solution. It's defined as the number of moles of solute per liter of solution. When you know the molarity, you can determine how much of a solute is present in a certain volume of a solution. The formula to calculate molarity is: \[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]To apply the concept of molarity, consider the problem: we have a 500.0 mL solution with a molarity of 2.80 M. First, convert 500.0 mL to liters by dividing by 1000, which gives 0.500 L. Then use the molarity formula to find the moles of KI:\[ \text{Moles of KI} = 2.80 \text{ M} \times 0.500 \text{ L} = 1.40 \text{ mol} \]This calculation shows how molarity helps determine the amount of solute (KI, in this case) in a given volume of solution.

Moles Calculation

Moles are a basic chemistry concept, used to count the number of entities, like atoms or molecules. In essence, one mole of any substance contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). To determine moles, use the formula:\[ \text{Moles} = \text{Molarity} \times \text{Volume in liters} \]In our problem, we calculated the moles of KI as follows:

• Molarity: 2.80 M
• Volume: 0.500 L

To find the moles, multiply the molarity by the volume:\[ \text{Moles of KI} = 2.80 \text{ mol/L} \times 0.500 \text{ L} = 1.40 \text{ mol} \]This step involves straightforward multiplication, which provides the amount of KI necessary for our solution's desired molarity and volume.

Molar Mass Determination

Molar mass is a crucial concept for converting between moles and grams. It represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). For a compound like potassium iodide (KI), it's the sum of the molar masses of its constituent elements.To determine the molar mass of KI:- Potassium (K) has a molar mass of 39.10 g/mol.- Iodine (I) has a molar mass of 126.90 g/mol.Add these two values together to get the molar mass of KI:\[ \text{Molar mass of KI} = 39.10 \text{ g/mol} + 126.90 \text{ g/mol} = 166.00 \text{ g/mol}\]Using this molar mass, you can find the mass of a solute in grams if you know its amount in moles. For instance, in our calculation, having 1.40 moles of KI results in:\[ \text{Mass of KI} = 1.40 \text{ mol} \times 166.00 \text{ g/mol} = 232.40 \text{ g} \]This enables the practical use of moles to prepare solutions in the laboratory.