Question

If a 45.3 -g sample of potassium nitrate is dissolved in enough water to make \(225 \mathrm{mL}\) of solution, what will be the molarity?

Short answer

The molarity of the potassium nitrate solution is \(1.99 \: \text{mol/L}\).

Step-by-step solution

Find the molar mass of potassium nitrate (KNO3)

To calculate the molar mass, we will add the atomic masses of each element in KNO3. Using the periodic table, we have: K (Potassium) = 39.10 g/mol N (Nitrogen) = 14.01 g/mol O (Oxygen) = 16.00 g/mol There are 1 potassium atom, 1 nitrogen atom, and 3 oxygen atoms in one molecule of potassium nitrate. Therefore, Molar mass of KNO3 = 39.10 + 14.01 + 3 * 16.00 = 101.11 g/mol

Determine the number of moles in the 45.3 g sample

We have the molar mass of potassium nitrate and the mass of the sample. We can now calculate the number of moles using the formula: moles = mass / molar mass So, the number of moles of KNO3 = (45.3 g) / (101.11 g/mol) = 0.448 moles

Convert the volume of the solution from mL to L

We are given the volume of solution as 225 mL. To convert it to liters, divide by 1000: Volume in liters = 225 mL / 1000 = 0.225 L

Calculate the molarity

Molarity is the number of moles of solute per liter of solution. Using the values we have found, we can calculate the molarity of the potassium nitrate solution as follows: Molarity = moles / volume in liters Molarity = 0.448 moles / 0.225 L = 1.99 mol/L Thus, the molarity of the potassium nitrate solution is 1.99 mol/L.

Key concepts

Molar Mass

Understanding molar mass is essential when studying chemistry, especially in calculations involving chemical reactions and solution preparation. Molar mass is defined as the mass of one mole of a substance, and it is expressed in grams per mole (g/mol). To determine the molar mass of a compound, such as potassium nitrate (KNO3), you add the atomic masses of each element in the compound according to its chemical formula.

For KNO3, you have one atom of potassium (K), one atom of nitrogen (N), and three atoms of oxygen (O). Using the atomic masses from the periodic table: potassium has an atomic mass of 39.10 g/mol, nitrogen is 14.01 g/mol, and oxygen is 16.00 g/mol. So, the calculation for the molar mass of KNO3 is:

• Potassium: 1 × 39.10 g/mol
• Nitrogen: 1 × 14.01 g/mol
• Oxygen: 3 × 16.00 g/mol

Adding these values yields the molar mass of KNO3, which is 101.11 g/mol. This molar mass allows you to convert between grams of KNO3 and moles, which is a common step in various chemical calculations.

Moles of Solute

The moles of solute in a solution denote the amount of a substance (solute) present in a given volume of solution. When it comes to calculating moles, the fundamental formula to keep in mind is:
\[ \text{{moles}} = \frac{{\text{{mass}}}}{{\text{{molar mass}}}} \]
It's crucial to measure the mass of the solute accurately and to know the molar mass of the solute. In our case, for a 45.3 g sample of potassium nitrate, the number of moles is calculated using its molar mass (101.11 g/mol). By dividing the mass of the sample by the molar mass, we find that there are 0.448 moles of potassium nitrate present in the solution. This step lays the foundation for subsequent calculations such as determining the solution's concentration.

Solution Concentration

Solution concentration expresses how much solute is present in a given quantity of solvent and is critical for precise scientific work, including laboratory experiments and medicine dosing. Molarity, one of the most common ways to express solution concentration, is defined as moles of solute per liter of solution (mol/L or M).

To compute molarity, you first convert the volume of solution from milliliters to liters, since molarity depends on liters. In our exercise with potassium nitrate, we convert the given volume of 225 mL to 0.225 L. Next, we use the formula:
\[ \text{{Molarity (M)}} = \frac{{\text{{moles of solute}}}}{{\text{{volume in liters}}}} \]
The molarity of our potassium nitrate solution is calculated by dividing the number of moles of solute (0.448 moles) by the volume of the solution in liters (0.225 L), resulting in 1.99 mol/L. This concentration tells us the strength of the solution and is used for further stoichiometric calculations or for preparing solutions with precise concentrations.

Stoichiometry

Stoichiometry is the aspect of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It's based on the law of conservation of mass and the notion that substances react in fixed ratios defined by their chemical formulas. When dealing with reactions in solution, stoichiometry intertwines with molarity calculations to determine how much of a reactant is needed or how much of a product is formed.

Knowing the molarity of solutions involved in a chemical reaction allows you to calculate the volume or mass of a solution required to react with a given amount of another substance. In stoichiometric calculations, it's often necessary to convert between moles and grams, or find the volume of a solution of known concentration that will provide the needed moles of solute for a reaction. By mastering stoichiometry, students can confidently engage in quantitative analysis and predict the outcomes of chemical reactions under various conditions.