Question

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

Short answer

The mass of KOH present in 35.0 mL of a 5.50 M solution is 10.80 grams.

Step-by-step solution

Convert Volume to Liters

The given volume of the solution is in milliliters. However, the unit of volume in molarity is liter. Therefore, we need to convert the volume from milliliters to liters. Since 1 L = 1000 mL, we have \(35.0 \, \text{mL} = 35.0 / 1000 = 0.035 \, \text{L}\)

Calculate the number of moles of KOH

Use the formula for molarity (M = moles/L) to find the number of moles in the solution. Since \(M = \text{moles} / \text{L}\),... we can find the number of moles by rearranging the formula as: moles = \(M \times \text{L}\). So, the moles of KOH = 5.50 M * 0.035 L = 0.1925 moles

Convert moles to grams

We'll use the molar mass of KOH to convert the amount from moles to grams. The molar mass of KOH is 56.105 g/mol. So, grams of KOH = moles * molar mass = 0.1925 moles * 56.105 g/mol = 10.80 g

Key concepts

Converting Milliliters to Liters

Understanding how to convert milliliters (mL) to liters (L) is critical for making precise calculations in chemistry, especially when dealing with solutions. One liter is equivalent to 1000 milliliters. The conversion is relatively straightforward: to convert milliliters to liters, you divide the number of milliliters by 1000.

For example, if you have 35.0 mL of a solution, and you want to know how many liters that is, you'd perform the following calculation: \[\begin{equation} 35.0\, \text{mL} = \frac{35.0}{1000} = 0.035\, \text{L} \end{equation}\]
. This step is paramount as molarity calculations require volumes in liters.

Molarity Formula

The molarity of a solution is one of the most common methods to express concentration. It is denoted by the symbol 'M' and is defined as the number of moles of solute per liter of solution. The formula for calculating molarity is:\[\begin{equation} M = \frac{\text{moles of solute}}{\text{liters of solution}} \end{equation}\]
. To find the molarity, you divide the moles of the solute by the volume of the solution in liters. Conversely, if molarity and volume are known, you can find the number of moles by rearranging the formula as: \[\begin{equation} \text{moles} = M \times \text{L} \end{equation}\]
. For instance, if a solution has a molarity of 5.50 M and there is 0.035 L of it, the number of moles would be calculated as 5.50 M multiplied by 0.035 L, giving you 0.1925 moles of the solute.

Molar Mass Conversion

After determining the number of moles of a substance, the next step is often to convert that quantity into grams. The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). Each element's molar mass can be found on the periodic table, and the molar mass of a compound is the sum of the individual molar masses of each element in it.

To convert moles to grams, you multiply the number of moles by the molar mass: \[\begin{equation} \text{grams} = \text{moles} \times \text{molar mass} \end{equation}\]
. So, if you have 0.1925 moles of KOH and the molar mass of KOH is 56.105 g/mol, you would calculate the grams of KOH as follows: \[\begin{equation} \text{grams of KOH} = 0.1925 \text{ moles} \times 56.105 \text{ g/mol} = 10.80 \text{ g} \end{equation}\]
. This conversion from moles to grams allows you to understand the actual amount of substance in a tangible form.