Question

How many moles and how many grams of the indicated solute does each of the following solutions contain? a. \(4.25 \mathrm{~L}\) of \(0.105 M \mathrm{KCl}\) solution b. \(15.1 \mathrm{~mL}\) of \(0.225 \mathrm{M} \mathrm{NaNO}_{3}\) solution c. \(25 \mathrm{~mL}\) of \(3.0 \mathrm{M} \mathrm{HCl}\) d. \(100 . \mathrm{mL}\) of \(0.505 M \mathrm{H}_{2} \mathrm{SO}_{4}\)

Short answer

a. The solution contains \(0.44625\) moles and \(33.27\) grams of KCl. b. The solution contains \(0.0033975\) moles and \(0.28879\) grams of NaNO3. c. The solution contains \(0.075\) moles and \(2.7345\) grams of HCl. d. The solution contains \(0.0505\) moles and \(4.95304\) grams of H2SO4.

Step-by-step solution

Calculate the moles of solute

To find the moles of solute in the solution, use the formula n = MV. Convert the volume to liters, then multiply it by the given molarity. n = (4.25 L) * (0.105 mol/L) = 0.44625 mol

Calculate the mass of solute

Now, find the molar mass of KCl: (39.10 g/mol for K) + (35.45 g/mol for Cl) = 74.55 g/mol. Multiply the moles by the molar mass to find the mass of the solute. mass = (0.44625 mol) * (74.55 g/mol) = 33.27 g b. \(15.1 mL\) of \(0.225 M NaNO_3\) solution

Calculate the moles of solute

To find the moles of solute in the solution, use the formula n = MV. Convert the volume to liters, then multiply it by the given molarity. n = (0.0151 L) * (0.225 mol/L) = 0.0033975 mol

Calculate the mass of solute

Now, find the molar mass of NaNO3: (22.99 g/mol for Na) + (14.01 g/mol for N) + (3 * 16.00 g/mol for O) = 85.00 g/mol. Multiply the moles by the molar mass to find the mass of the solute. mass = (0.0033975 mol) * (85.00 g/mol) = 0.28879 g c. \(25 mL\) of \(3.0 M HCl\)

Calculate the moles of solute

To find the moles of solute in the solution, use the formula n = MV. Convert the volume to liters, then multiply it by the given molarity. n = (0.025 L) * (3.0 mol/L) = 0.075 mol

Calculate the mass of solute

Now, find the molar mass of HCl: (1.01 g/mol for H) + (35.45 g/mol for Cl) = 36.46 g/mol. Multiply the moles by the molar mass to find the mass of the solute. mass = (0.075 mol) * (36.46 g/mol) = 2.7345 g d. \(100. mL\) of \(0.505 M H_2SO_4\)

Calculate the moles of solute

To find the moles of solute in the solution, use the formula n = MV. Convert the volume to liters, then multiply it by the given molarity. n = (0.100 L) * (0.505 mol/L) = 0.0505 mol

Calculate the mass of solute

Now, find the molar mass of H2SO4: (2 * 1.01 g/mol for H) + (32.07 g/mol for S) + (4 * 16.00 g/mol for O) = 98.08 g/mol. Multiply the moles by the molar mass to find the mass of the solute. mass = (0.0505 mol) * (98.08 g/mol) = 4.95304 g

Key concepts

Moles of Solute

To understand how many moles of solute are present in a solution, the concept of molarity is fundamental. Molarity (M) tells us how concentrated a solution is, using units of moles of solute per liter of solution. The formula used to calculate moles (n) from molarity is:

• \( n = M \times V \)

Here, M represents molarity and V is the volume of the solution in liters. Remember to convert any milliliters to liters before using this formula, by dividing the milliliters by 1000. This conversion is essential to ensure that the units are consistent. By multiplying the molarity by the volume in liters, you derive the moles of solute contained in the solution. The moles give us an indication of the number of molecules or atoms present, helping us understand the amount of substance dissolved.

Mass Calculation

After determining the moles of solute in a solution, the next step often involves calculating the mass of that solute. This involves using the molar mass of the substance, which is the sum of the atomic masses of all atoms in a molecule in grams per mole. The formula to find the mass (mass) is:

• \( \text{mass} = n \times \text{molar mass} \)

Where n is the number of moles of the solute and "molar mass" is the mass of one mole of that particular solute. Multiplying these two gives us the mass of the solute in grams. This step is crucial in knowing how much solid solute was initially dissolved to make the solution.

Molar Mass

Molar mass is an essential concept when dealing with chemical solutions, especially for mass calculation. It represents the mass of one mole of a compound. The unit used is grams per mole (g/mol). To determine the molar mass, add together the atomic masses of each element present in the compound. For example, for KCl:

• Potassium (K) has an atomic mass of roughly 39.10 g/mol
• Chlorine (Cl) has an atomic mass of 35.45 g/mol

So, the molar mass of KCl becomes:

• \( 39.10 + 35.45 = 74.55 \text{ g/mol} \)

A clear understanding of molar mass is key to converting between moles of solute and grams.

Solution Concentration

Solution concentration is described by molarity, which quantifies the amount of solute in a given volume of solution. It is expressed in the units of moles per liter. Molarity is calculated using the formula:

• \( M = \frac{n}{V} \)

Where n is the moles of solute and V is the volume of the solution in liters. By knowing the molarity, we can easily determine how concentrated a solution is. Concentration affects various chemical and physical properties, such as boiling point, freezing point, and electrical conductivity, making it critical in laboratory and industrial applications. Understanding molarity helps in preparing solutions with the desired properties and concentrations.