Question

How many moles of the indicated solute does each of the following solutions contain? a. \(4.25 \mathrm{~mL}\) of \(0.105 \mathrm{M} \mathrm{CaCl}_{2}\) solution b. \(11.3 \mathrm{~mL}\) of \(0.405 \mathrm{M} \mathrm{NaOH}\) solution c. \(1.25 \mathrm{~L}\) of \(12.1 \mathrm{M} \mathrm{HCl}\) solution d. \(27.5 \mathrm{~mL}\) of \(1.98 \mathrm{M} \mathrm{NaCl}\) solution

Short answer

The short answers for the moles of solute in each solution are: a. \(0.00044625 \mathrm{~mol\, CaCl}_{2}\) b. \(0.0045745 \mathrm{~mol\, NaOH}\) c. \(15.125 \mathrm{~mol\, HCl}\) d. \(0.05445 \mathrm{~mol\, NaCl}\)

Step-by-step solution

1. Convert volume to liters

Since the volume of the solution is given in milliliters, we need to convert it to liters: 4.25 mL = 4.25/1000 L = 0.00425 L

2. Calculate moles of solute

Now, let's find the moles of solute using the formula: Moles of solute = Volume of solution (L) × Molarity = 0.00425 L × 0.105 M = 0.00044625 mol CaCl2 #b. 11.3 mL of 0.405 M NaOH solution#

1. Convert volume to liters

Convert the volume from milliliters to liters: 11.3 mL = 11.3/1000 L = 0.0113 L

2. Calculate moles of solute

Find the moles of solute using the formula: Moles of solute = Volume of solution (L) × Molarity = 0.0113 L × 0.405 M = 0.0045745 mol NaOH #c. 1.25 L of 12.1 M HCl solution#

1. Convert volume to liters

The volume is already given in liters: 1.25 L

2. Calculate moles of solute

Find the moles of solute using the formula: Moles of solute = Volume of solution (L) × Molarity = 1.25 L × 12.1 M = 15.125 mol HCl #d. 27.5 mL of 1.98 M NaCl solution#

1. Convert volume to liters

Convert the volume from milliliters to liters: 27.5 mL = 27.5/1000 L = 0.0275 L

2. Calculate moles of solute

Find the moles of solute using the formula: Moles of solute = Volume of solution (L) × Molarity = 0.0275 L × 1.98 M = 0.05445 mol NaCl

Key concepts

Molarity

Molarity is an essential concept when dealing with solutions in chemistry. It helps us understand how much solute (the substance being dissolved) is present in a particular volume of solution. The molarity is expressed as moles of solute per liter of solution. This is denoted by the symbol 'M'. For example, when we say a solution has a molarity of 0.105 M, it means there are 0.105 moles of solute in every liter of the solution.

To calculate molarity, use the formula:

• Molarity (M) = Moles of Solute / Volume of Solution (L)

This formula helps you determine the concentration of a solution, which is crucial for reactions, dilutions, and determining how to mix substances in chemistry.

Volume Conversion

Volume conversion is a vital part of solving molarity problems. In chemistry, volumes are frequently given in milliliters (mL), but calculations often require the volume in liters (L).

To convert milliliters to liters, simply divide the number of milliliters by 1,000. This is because 1 liter is equivalent to 1,000 milliliters. So, for example, if you have 4.25 mL, you convert it to liters as follows:

\[4.25 \, \text{mL} = \frac{4.25}{1000} \, \text{L} = 0.00425 \, \text{L}\]
By converting the volume to liters, you can accurately use the molarity formula to find the number of moles of the solute. This conversion is straightforward but essential in carrying out accurate and meaningful calculations in solution chemistry.

Solution Chemistry

Solution chemistry revolves around understanding how substances dissolve and interact in a solvent, typically water. The main focus is on the interactions that occur on a molecular level when substances are mixed to form a solution.

Key elements of solution chemistry include:

• **Solute:** the substance that is dissolved in the solvent.
• **Solvent:** the liquid in which the solute is dissolved. In many cases, this is water.
• **Concentration:** measures how much solute is present in a given amount of solvent or solution, with molarity being a common unit.

Understanding solution chemistry is crucial for calculating quantities like the number of moles of a solute, which is often required to carry out reactions or to prepare solutions with specific concentrations.

Furthermore, knowing how a solute behaves in a solvent can help predict physical properties like boiling and freezing points and the solution's overall behavior in different chemical reactions.