Question

The number of moles of \(\mathrm{KCl}\) in \(1000 \mathrm{~mL}\) of 3 molar solution is: (a) 2 (b) 3 (c) 4 (d) 6

Short answer

The number of moles of KCl is 3.

Step-by-step solution

Understanding Molarity

Molarity, also known as molar concentration, is defined as the number of moles of solute per liter of solution. It is expressed as M = n/V, where M is molarity, n is the number of moles of solute, and V is the volume of the solution in liters.

Identify Given Values

From the problem, we know the following: 1. The molarity (M) of the solution is 3 mol/L. 2. The volume (V) of the solution is 1000 mL, which is equivalent to 1 L since there are 1000 mL in a liter.

Use Molarity Formula

Using the formula for molarity, M = n/V, we can determine the number of moles by rearranging the formula to solve for n: n = M × V.

Calculate Number of Moles

Substitute the known values into the rearranged formula: \[ n = 3 ext{ mol/L} imes 1 ext{ L} = 3 ext{ moles} \]

Conclusion

The number of moles of \( ext{KCl}\) in 1000 mL of a 3 molar solution is 3.

Key concepts

Moles of solute

A mole is a unit in chemistry that helps us measure the amount of substance. It's somewhat similar to how we use dozens to count items. For example, one mole of any substance contains Avogadro's number of entities, which is roughly \(6.022 \times 10^{23}\) particles, like atoms or molecules. In our problem, the moles of solute specifically refer to the amount of potassium chloride (\(\text{KCl}\)) present in the solution. The term "solute" here means the substance dissolved in a liquid, forming a solution. When you say you have 3 moles of \(\text{KCl}\), it means you have \(3 \times 6.022 \times 10^{23}\) formula units of this compound. It's important to know how many moles of a solute are present because this helps in determining the solution's properties such as concentration, and how it will react in a chemical equation. To calculate the moles of solute, you often rearrange the molarity equation as shown: \[ n = M \times V \].This equation lets you find out how much solute (in moles) is in a specific volume of solution, which in our exercise is a liter.

Molar concentration

Molarity is a way to express concentration in chemistry. It tells us how much solute is in a certain volume of solution. The unit of molarity is molar, often symbolized by "M" - defined as moles of solute per liter of solution.

• The formula for molarity is \( M = \frac{n}{V} \), where \(n\) is the moles of solute and \(V\) is the volume in liters.
• Higher molarity means a more concentrated solution; lower molarity signifies a diluted one.

In our exercise, the molarity is given as 3 molar, meaning there are 3 moles of solute in every liter of solution. This clarity is crucial since it allows scientists to replicate experiments and maintain consistent conditions, which is particularly important in fields like medicine and pharmacology.To determine the concentration of any unknown solution, knowing its molarity helps chemists adjust the amounts of various chemicals accurately and safely. It is another critical aspect of stoichiometry, which is the area of chemistry that deals with the quantitative relationships in chemical reactions.

Solution volume

Volume is a measure of the space that a substance or an object occupies. In chemistry, when we're dealing with solutions, volume becomes a crucial factor in describing its concentration. As discussed in the solution, we are working with a volume of 1000 mL or 1 liter. A milliliter is another unit of volume measurement often used in liquid solutions. Since solutions in chemistry are usually expressed in liters (the SI unit for volume), converting milliliters to liters is common practice - where 1000 mL equals 1 L. Understanding solution volume is essential because it helps determine how many moles of solute can dissolve in the solution.

• A larger volume can dissolve more solute if the solution's saturation point is not reached.
• Conversely, a concentrated solution has a smaller volume but maintains a higher amount of solute.

By controlling volume and knowing molarity, one can compute the precise amount of solute needed, ensuring the solution's concentration remains consistent in experiments or productions. This knowledge is vital in laboratories, industries, and everyday tasks that involve solutions.