Question

Calculate the molar concentration for each of the following solutions. (a) \(1.00 \mathrm{~g} \mathrm{KCl}\) in \(75.0 \mathrm{~mL}\) of solution (b) \(1.00 \mathrm{~g} \mathrm{Na}_{2} \mathrm{CrO}_{4}\) in \(75.0 \mathrm{~mL}\) of solution (c) \(20.0 \mathrm{~g} \mathrm{MgBr}_{2}\) in \(250.0 \mathrm{~mL}\) of solution (d) \(20.0 \mathrm{~g} \mathrm{Li}_{2} \mathrm{CO}_{3}\) in \(250.0 \mathrm{~mL}\) of solution

Short answer

(a) 0.179 M, (b) 0.0824 M, (c) 0.435 M, (d) 1.08 M

Step-by-step solution

Calculate moles of solute (a)

First, find the molar mass of KCl by summing the atomic masses: K = 39.10 g/mol, Cl = 35.45 g/mol. Therefore, the molar mass of KCl is 74.55 g/mol. Calculate the moles of KCl: \[ \text{moles of KCl} = \frac{1.00 \text{ g}}{74.55 \text{ g/mol}} \approx 0.0134 \text{ moles} \]

Calculate molarity of solution (a)

Convert volume from mL to L: 75.0 mL = 0.075 L. Use the formula for molarity: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in L}} \] So, \[ M = \frac{0.0134 \text{ moles}}{0.075 \text{ L}} \approx 0.179 \text{ M} \]

Calculate moles of solute (b)

Find the molar mass of Na₂CrO₄: Na = 22.99 g/mol, Cr = 51.996 g/mol, O = 16.00 g/mol. Molar mass of Na₂CrO₄ = (2 × 22.99) + 51.996 + (4 × 16.00) = 161.98 g/mol. Calculate moles of Na₂CrO₄: \[ \text{moles of Na₂CrO₄} = \frac{1.00 \text{ g}}{161.98 \text{ g/mol}} \approx 0.00618 \text{ moles} \]

Calculate molarity of solution (b)

Use the previously converted volume: 75.0 mL = 0.075 L. Calculate molarity: \[ M = \frac{0.00618 \text{ moles}}{0.075 \text{ L}} \approx 0.0824 \text{ M} \]

Calculate moles of solute (c)

Calculate the molar mass of MgBr₂: Mg = 24.305 g/mol, Br = 79.904 g/mol. Molar mass of MgBr₂ = 24.305 + (2 × 79.904) = 184.114 g/mol. Calculate moles of MgBr₂: \[ \text{moles of MgBr₂} = \frac{20.0 \text{ g}}{184.114 \text{ g/mol}} \approx 0.1087 \text{ moles} \]

Calculate molarity of solution (c)

Convert volume from mL to L: 250.0 mL = 0.250 L. Calculate molarity: \[ M = \frac{0.1087 \text{ moles}}{0.250 \text{ L}} \approx 0.435 \text{ M} \]

Calculate moles of solute (d)

Find the molar mass of Li₂CO₃: Li = 6.94 g/mol, C = 12.01 g/mol, O = 16.00 g/mol. Molar mass of Li₂CO₃ = (2 × 6.94) + 12.01 + (3 × 16.00) = 73.89 g/mol. Calculate moles of Li₂CO₃: \[ \text{moles of Li₂CO₃} = \frac{20.0 \text{ g}}{73.89 \text{ g/mol}} \approx 0.2707 \text{ moles} \]

Calculate molarity of solution (d)

Use the converted volume: 250.0 mL = 0.250 L. Calculate molarity: \[ M = \frac{0.2707 \text{ moles}}{0.250 \text{ L}} \approx 1.08 \text{ M} \]

Key concepts

Moles of Solute

Understanding moles is crucial in chemistry, especially when working with solutions. A mole is essentially a count of a specific number of molecules or atoms – precisely, Avogadro's number, which is approximately \(6.022 \times 10^{23}\). To calculate the moles of solute, you need two pieces of information: the mass of the solute and its molar mass.
Here’s what you do step-by-step:

• Find the molar mass by adding up the atomic masses of all the atoms in a molecule of the solute. For example, in potassium chloride (KCl), the molar mass is the sum of potassium (39.10 g/mol) and chlorine (35.45 g/mol), resulting in 74.55 g/mol.
• Use the formula: \( \text{moles of solute} = \frac{\text{mass of solute (g)}}{\text{molar mass (g/mol)}} \). This formula allows you to determine the number of moles from a given mass of solute.

Finding moles is the first step in understanding how concentrated a solution is.

Molarity Calculation

Molarity, often represented by the symbol \( M \), is a measure of concentration in solutions. It is defined as moles of solute per liter of solution. When you're tasked with finding the molarity, you need to have calculated the moles of solute and be able to convert the solution’s volume into liters.
Follow these steps:

• Convert the volume of your solution from milliliters to liters by dividing by 1000 since there are 1000 mL in a liter. For example, 75.0 mL of solution is equivalent to 0.075 L.
• Use the molarity formula: \( M = \frac{\text{moles of solute}}{\text{volume of solution in L}} \). This tells you how much solute is present in a unit volume of solution, which is vital for understanding how `strong` or `weak` a solution is.

Molarity gives you a straightforward way to express and use the concentration in chemical reactions and solutions.

Molar Mass Calculation

Molar mass plays a key role in bridging the amount of substance you have with the number of moles it contains, which is essential for making calculations in chemistry. It effectively helps in converting grams to moles and vice versa.
To calculate molar mass, you:

• Identify each element in the compound and use the periodic table to find its atomic mass. For example, in the compound \(\text{MgBr}_2\), magnesium (Mg) has an atomic mass of 24.305 g/mol and bromine (Br) has an atomic mass of 79.904 g/mol.
• Multiply the atomic mass of each element by the number of times the element appears in the compound (e.g., bromine appears twice in \(\text{MgBr}_2\)).
• Add up all these values to get the molar mass of the compound. So, \(\text{MgBr}_2\) would have a molar mass of 24.305 + (2 × 79.904) = 184.114 g/mol.

Understanding molar mass allows you to convert between mass and moles, making it vital for any stoichiometric calculations.