Question

How many grams of $\mathrm{KOH}$ are present in $35.0\mathrm{mL}$ of a $5.50\mathrm{M}\mathrm{KOH}$ solution?

Short answer

There are 10.80 grams of KOH in the solution.

Step-by-step solution

Calculate the Moles of KOH

To find the grams of KOH present in the solution, we first need to determine the number of moles. Molarity (M) is defined as moles of solute per liter of solution. Using the formula: $extMolesofKOH=extMolarityimesextVolumeinLiters$, we convert the volume from milliliters to liters: $35.0\text{ mL}=0.035\text{ L}$. Therefore, the moles of KOH are: $5.50extMimes0.035extL=0.1925\text{ moles}$.

Calculate Grams of KOH

Now that we have the moles of KOH, we multiply by its molar mass to find the grams. The molar mass of KOH (Potassium Hydroxide) is calculated as: K (39.10 g/mol) + O (16.00 g/mol) + H (1.01 g/mol) = 56.11 g/mol. Therefore, the grams of KOH are: $0.1925\text{ moles}\times 56.11\text{ g/mol}=10.80\text{ grams}$.

Key concepts

Solution Stoichiometry

Solution stoichiometry involves calculating the quantities of reactants or products in a chemical reaction that occurs in a solution. It helps us understand the relationship between the concentrations of substances involved. This is crucial in various fields, from chemistry labs to industrial applications.
When we talk about molarity, we refer to the concentration of a solute in a solution. Molarity is expressed in "moles per liter," denoting the number of moles of solute present in a given volume of solution.
In our exercise, we're given a molarity of KOH solution and a volume in milliliters. Our task is to first determine how many moles of KOH are in that particular volume using the molarity formula. Understanding this principle allows us to convert between volumes and moles, enabling precise manipulation in chemical processes.

Moles Calculation

The calculation of moles is a fundamental concept in chemistry that relates the amount of a substance to its chemical formula.
Moles provide a standard measure to express amounts of a chemical substance, allowing scientists to express how many atoms, ions, or molecules are involved in a given process. To determine the moles of a solute from a solution's molarity, use this formula:

• Moles = Molarity (M) × Volume (L)

In the given problem, we start by converting milliliters to liters, since molarity is defined per liter. For a 35.0 mL solution, this conversion gives us 0.035 L. The next step is a straightforward multiplication of the molarity (5.50 M) by the converted volume, giving the number of moles of KOH present in the solution as 0.1925 moles. This forms the basis for subsequent calculations, such as finding the mass of the compound.

Molar Mass Calculation

Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It's calculated by summing the atomic masses of all atoms in a molecule. This information is essential for converting moles of a substance to grams, which is often required in practical scenarios.
In our exercise, the molar mass of Potassium Hydroxide (KOH) is calculated by adding the atomic masses of Potassium (K), Oxygen (O), and Hydrogen (H):

• Potassium (K): 39.10 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol

Total molar mass of KOH = 56.11 g/mol.
Armed with the number of moles (0.1925 moles) from our earlier calculation, we multiply by the molar mass to find the total grams of KOH in the solution: 0.1925 moles × 56.11 g/mol = 10.80 grams. Understanding molar mass helps link molecular weight with laboratory measurements, making it a key tool in chemical analysis and synthesis.