Question

What \(mass\) of the indicated solute does each of the following solutions contain? a. \(2.50 \mathrm{~L}\) of \(13.1 \mathrm{M} \mathrm{HCl}\) solution b. \(15.6 \mathrm{~mL}\) of \(0.155 \mathrm{M} \mathrm{NaOH}\) solution c. \(135 \mathrm{~mL}\) of \(2.01 \mathrm{M} \mathrm{HNO}_{3}\) solution d. 4.21 L of \(0.515 M \mathrm{CaCl}_{2}\) solution

Short answer

The mass of solute in each solution is: a. \(1,195.375 \mathrm{g}\) of \(\mathrm{HCl}\) b. \(0.09672 \mathrm{g}\) of \(\mathrm{NaOH}\) c. \(17.09305 \mathrm{g}\) of \(\mathrm{HNO}_{3}\) d. \(240.56465 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\)

Step-by-step solution

Calculate moles of solute in each solution

We will use the molarity formula M = moles solute / Volume solution for each solution. a. moles of HCl in 2.50 L of 13.1 M HCl solution: moles HCl = M * Volume = 13.1 M * 2.50 L = 32.75 moles HCl b. moles of NaOH in 15.6 mL of 0.155 M NaOH solution: moles NaOH = M * Volume = 0.155 M * 0.0156 L (convert from mL to L) = 0.002418 moles NaOH c. moles of HNO3 in 135 mL of 2.01 M HNO3 solution: moles HNO3 = M * Volume = 2.01 M * 0.135 L (convert mL to L) = 0.27135 moles HNO3 d. moles of CaCl2 in 4.21 L of 0.515 M CaCl2 solution: moles CaCl2 = M * Volume = 0.515 M * 4.21 L = 2.16815 moles CaCl2

Calculate molar mass of each solute

We will find the molar mass of each solute using their chemical formulas and the periodic table. a. Molar mass of HCl = 1 (H) + 35.5 (Cl) = 36.5 g/mol b. Molar mass of NaOH = 23 (Na) + 16 (O) + 1 (H) = 40 g/mol c. Molar mass of HNO3 = 1 (H) + 14 (N) + 3 * 16 (O) = 63 g/mol d. Molar mass of CaCl2 = 40 (Ca) + 2 * 35.5 (Cl) = 111 g/mol

Calculate the mass of solute in each solution

We will use the moles of solute and their molar mass to find the mass of solute in each solution. a. Mass of HCl = moles HCl * molar mass HCl = 32.75 moles * 36.5 g/mol = 1,195.375 g b. Mass of NaOH = moles NaOH * molar mass NaOH = 0.002418 moles * 40 g/mol = 0.09672 g c. Mass of HNO3 = moles HNO3 * molar mass HNO3 = 0.27135 moles * 63 g/mol = 17.09305 g d. Mass of CaCl2 = moles CaCl2 * molar mass CaCl2 = 2.16815 moles * 111 g/mol = 240.56465 g So, the mass of solute in each solution is: a. 1,195.375 g of HCl b. 0.09672 g of NaOH c. 17.09305 g of HNO3 d. 240.56465 g of CaCl2

Key concepts

Mole Concept

Understanding the mole concept is essential for performing accurate calculations in chemistry. The mole is a unit used to measure the amount of a substance, specifically to count particles like atoms, molecules, or ions. It is one of the fundamental concepts in chemistry because it allows chemists to relate the microscopic world of individual atoms and molecules to the macroscopic world we can measure.

One mole is defined as exactly 6.022 x 10^23 particles (Avogadro's number), which corresponds to the number of atoms in 12 grams of carbon-12. When we say we have 1 mole of a substance, we are indicating that we have 6.022 x 10^23 units of that substance, whether they be atoms, molecules, or ions.

To connect this to molarity calculations: when you're given the molarity of a solution, you can find the number of moles of the solute in a given volume of solution. For instance, if you have a 2.00 M H2SO4 solution, this means every liter of that solution contains 2.00 moles of H2SO4. To find the total moles in 3 liters of this solution, you would multiply the molarity (2.00 M) by the volume in liters (3 L) to obtain 6.00 moles of H2SO4.

Chemical Solutions

Chemical solutions play a critical role in various scientific and industrial processes. They are defined as homogeneous mixtures composed of a solute (the substance being dissolved) and a solvent (the substance doing the dissolving). In chemistry, the most common solvent is water, but solvents can be gases, liquids, or solids.

The concentration of a solution is a measure of how much solute is dissolved in a certain amount of solvent. Molarity (M) is one of the ways to express concentration and it is expressed in molar, which is moles of solute per liter of solution. It's important because it allows chemists to accurately prepare solutions for reactions and to calculate how much of a substance is present in a solution.

By improving the exercise to consider different concentrations and volumes of solutes, students can apply the molarity concept better. It reinforces the relationship between the volume of the solution, the concentration of the solution (molarity), and the amount of solute in moles. Considering a variety of scenarios, such as dilution or mixing solutions, could provide a deeper comprehension of how molarity changes with these processes.

Molar Mass

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The unit for molar mass is grams per mole (g/mol), and it tells us how many grams are in one mole of that substance. To calculate the molar mass of a compound, you sum the molar masses of all the atoms in the molecule.

For example, water (H2O) has a molar mass of approximately 18 g/mol, calculated by adding the molar masses of two hydrogen atoms (1 g/mol each) to one oxygen atom (16 g/mol). This means that one mole of water weighs 18 grams.

In molarity calculations, knowing the molar mass allows for the conversion between the mass of a substance and the number of moles. When solving an exercise that involves finding the mass of a solute in a solution, the molar mass provides the critical link between the solution's volume (and molarity) and the solute's mass, ensuring a proper understanding of how these quantities relate.