Question

What mass of the indicated solute does each of the following solutions contain? a. 2.50 L of $13.1M$ 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 $0.515M{\mathrm{CaCl}}_2$ solution

Short answer

The mass of solute in each solution is as follows: a. $1190.195\mathrm{g}$ of HCl b. $0.09612\mathrm{g}$ of NaOH c. $17.078085\mathrm{g}$ of HNO3 d. $237.34923\mathrm{g}$ of CaCl2

Step-by-step solution

Determine the volume in liters

In this case, the volume is already given in liters: 2.50 L.

Calculate the molar mass of HCl

Using the periodic table: H = 1.01 g/mol Cl = 35.45 g/mol Molar mass of HCl = 1.01 + 35.45 = 36.46 g/mol

Calculate the mass of HCl

Using the formula: Mass of HCl = (2.50 L) × (13.1 mol/L) × (36.46 g/mol) = 1190.195 g #b. 15.6 mL of 0.155 M NaOH solution#

Determine the volume in liters

Convert the volume from mL to L: 15.6 mL × (1 L / 1000 mL) = 0.0156 L

Calculate the molar mass of NaOH

Using the periodic table: Na = 22.99 g/mol O = 16.00 g/mol H = 1.01 g/mol Molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol

Calculate the mass of NaOH

Using the formula: Mass of NaOH = (0.0156 L) × (0.155 mol/L) × (40.00 g/mol) = 0.09612 g #c. 135 mL of 2.01 M HNO3 solution#

Determine the volume in liters

Convert the volume from mL to L: 135 mL × (1 L / 1000 mL) = 0.135 L

Calculate the molar mass of HNO3

Using the periodic table: H = 1.01 g/mol N = 14.01 g/mol O = 16.00 g/mol Molar mass of HNO3 = 1.01 + 14.01 + (3 × 16.00) = 63.01 g/mol

Calculate the mass of HNO3

Using the formula: Mass of HNO3 = (0.135 L) × (2.01 mol/L) × (63.01 g/mol) = 17.078085 g #d. 4.21 L of 0.515 M CaCl2 solution#

Determine the volume in liters

In this case, the volume is already given in liters: 4.21 L.

Calculate the molar mass of CaCl2

Using the periodic table: Ca = 40.08 g/mol Cl = 35.45 g/mol Molar mass of CaCl2 = 40.08 + (2 × 35.45) = 110.98 g/mol

Calculate the mass of CaCl2

Using the formula: Mass of CaCl2 = (4.21 L) × (0.515 mol/L) × (110.98 g/mol) = 237.34923 g

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed. Central to stoichiometry is the mole concept, which links the mass of a substance to the number of its particles, typically atoms, molecules, or ions.

When solving stoichiometric problems, you often use a balanced chemical equation to understand the ratios in which the reactants combine to form products. However, in the case of preparing solutions, stoichiometry involves calculating the mass of a solute needed to achieve a specific concentration in a given volume of solvent. This concept is fundamental in chemistry because it lets us predict amounts of substances required or produced — critical for everything from cooking to pharmaceuticals.

Always remember to start by identifying the relevant chemical equation and the information you've been given. This way, you can set up a stoichiometric conversion to transition smoothly between units and determine the mass of your substance of interest.

Converting Volume to Moles

When tackling chemistry problems, you’ll often need to convert the volume of a liquid solution to the number of moles of solute it contains. This process is critical in stoichiometry, especially when the solution's molarity is known. Molarity is a concentration unit defined as the number of moles of solute per liter of solution (mol/L).

To convert the volume of a solution to moles, you can use the formula:
Number of moles = Volume (L) × Molarity (mol/L).
This conversion forms the basis for many calculations in chemistry, such as determining the mass of a solute in a solution. Just ensure that the volume is in liters before performing the calculation. If the volume is given in milliliters or any other unit, convert it to liters first by dividing by 1000, since there are 1000 milliliters in a liter.

Molarity and Solution Preparation

Molarity is a critical component in solution preparation and is extensively used in chemistry to convey the concentration of a solute within a solution. Defined as moles of solute per liter of solution, molarity allows chemists to work with meaningful quantities, given that a mole represents a set number of particles or entities, typically Avogadro's number (6.022×10²³).

To prepare a solution of specific molarity, you would:

• Dissolve the calculated mass of solute into a volume of solvent to achieve the desired concentration.
• Measure the correct volume of the solvent, typically water.
• Finally, add the solute and dissolve it fully, adjusting the volume as needed to account for any changes in solution level.

By mastering molarity, students can better understand reaction rates, reagent quantities, and how to mix solutions accurately in laboratory settings.

Chemical Formula and Molar Mass

The chemical formula of a compound tells you which elements and how many atoms of each are present in a molecule. This information is invaluable when it comes to calculating the molar mass — the mass of one mole of substance. The molar mass is obtained by summing the atomic masses of all the atoms present in the formula, with each element's atomic mass taken from the periodic table, measured in grams per mole (g/mol).

Knowing the molar mass is essential for converting between mass and moles, which is a routine part of many stoichiometric calculations. For example, in molarity calculations, the molar mass allows you to calculate the mass of the solute needed to create a solution of a specific concentration. A solid grasp of how to determine molar mass from a chemical formula facilitates not only stoichiometry problems but also helps in understanding the physical properties of the substance, such as density and molecular weight.