Question

Calculate the molarity of a solution that contains (a) \(2.00 \times 10^{-3}\) mol cobalt(II) sulfate in \(35.0 \mathrm{~mL}\) of solution. (b) 2.75 mole potassium hydroxide in a total volume of \(135 \mathrm{~mL}\) of solution.

Short answer

The molarity of the cobalt(II) sulfate solution is approximately 0.0571 M. The molarity of the potassium hydroxide solution is approximately 20.37 M.

Step-by-step solution

Understand Molarity

Molarity is a measure of the concentration of a solute in a solution and is defined as the number of moles of solute divided by the volume of the solution in liters. The formula for molarity (M) is: M = moles of solute/volume of solution in liters.

Convert milliliters to liters for cobalt(II) sulfate

Since molarity is moles per liter, you need to convert the volume of the solution from milliliters to liters. To do this, use the conversion factor 1 liter = 1000 milliliters. For cobalt(II) sulfate, the volume in liters is: 35.0 mL x (1 L/1000 mL) = 0.035 L.

Calculate molarity for cobalt(II) sulfate

Use the formula M = moles/liters to find the molarity of cobalt(II) sulfate. Substitute the known values: M = (2.00 x 10^{-3} mol) / (0.035 L) to get the molarity.

Convert milliliters to liters for potassium hydroxide

Similarly, for potassium hydroxide, convert the volume from milliliters to liters. The volume in liters is: 135 mL x (1 L/1000 mL) = 0.135 L.

Calculate molarity for potassium hydroxide

For potassium hydroxide, use the molarity formula M = moles/liters. Substitute the known values: M = (2.75 mol) / (0.135 L) to find the molarity.

Key concepts

Concentration of Solution

The concentration of a solution is a measure of how much solute is dissolved in a given quantity of solvent. Understand it like a recipe: if you add more sugar to your tea, it gets sweeter; similarly, adding more solute to a solution makes it more concentrated. In chemistry, molarity is one widely used unit to express concentration. It is denoted by 'M' and describes the number of moles of solute per liter of solution. When calculating the molarity, it's like figuring out how strong your tea is based on the amount of sugar and the total tea volume.

When working through textbook problems, it is essential to follow units carefully. Converting to the correct units before using the molarity formula is crucial for accuracy. For example, to calculate the molarity of a sugar solution, you would divide the number of moles of sugar by the solution's volume in liters. This results in a figure that effectively communicates to others in the field exactly 'how sweet' your solution is.

Moles to Liters Conversion

Since molarity depends on the volume of the solution being in liters, converting from milliliters to liters is a frequent and necessary step for accurate calculations. It's common to encounter volumes in milliliters (mL) when dealing with laboratory solutions; however, molarity calculations need volumes in liters (L) for standardization.

The process is straightforward: there are 1000 milliliters in 1 liter. To convert, simply divide your milliliter measurement by 1000. For instance, if you have 250 mL of a solution, this is equivalent to 0.250 L after conversion. Picture this as repackaging a large number of small water bottles into a few large ones -- you're simply changing the units but the total amount of water remains the same. Always ensure the conversion is done before plugging the volume into the molarity formula to avoid any mix-up and ensure precise results.

Solute and Solvent

In any solution, there are two key players: the solute and the solvent. The solute is the substance that is being dissolved, like the sugar or salt you might stir into water. The solvent is the substance that does the dissolving, typically the component in larger amount; in many cases, it's water. Imagine you're making lemonade—the sugar would be the solite, and the water would be the solvent. When combined, they create a sweet drink, or in chemical terms, a solution.

In the context of molarity, the solute is crucial because it's the substance whose amount in moles is being measured per liter of solution. Understanding the distinction between solute and solvent is foundational when it comes to preparing solutions and performing calculations associated with them.