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Chapter 4: Problem 57

Calculate the molarity of each of the following solutions: (a) \(29.0 \mathrm{~g}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(545 \mathrm{~mL}\) of solution, (b) \(15.4 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) in \(74.0 \mathrm{~mL}\) of solution, (c) \(9.00 \mathrm{~g}\) of sodium chloride \((\mathrm{NaCl})\) in \(86.4 \mathrm{~mL}\) of solution.

Short Answer

Expert verified
(a) 1.15 M, (b) 0.608 M, (c) 1.78 M.

Step by step solution

01

Understand Molarity Formula

Molarity (M) is defined as moles of solute per liter of solution. The formula is:\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \] To find the molarity, first calculate the moles of solute and convert the volume from milliliters to liters.
02

Calculate Moles of Ethanol

First, calculate the molar mass of ethanol \((\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH})\). It is calculated as:\[ 2(12.01) + 6(1.008) + 16.00 = 46.08 \text{ g/mol} \]Now, calculate moles of ethanol by dividing the given mass by the molar mass:\[ 29.0 \text{ g} \times \frac{1 \text{ mol}}{46.08 \text{ g}} = 0.629 \text{ mol} \]
03

Calculate Volume in Liters for Ethanol Solution

Convert the given volume from milliliters to liters:\[ 545 \, \text{mL} = 0.545 \, \text{L} \]
04

Calculate Molarity of Ethanol Solution

Substitute the values into the molarity formula:\[ M = \frac{0.629 \, \text{mol}}{0.545 \, \text{L}} \approx 1.15 \, \text{M} \]
05

Calculate Moles of Sucrose

First, calculate the molar mass of sucrose \((\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11})\). It is calculated as:\[ 12(12.01) + 22(1.008) + 11(16.00) = 342.30 \text{ g/mol} \]Now, calculate moles of sucrose by dividing the given mass by the molar mass:\[ 15.4 \, \text{g} \times \frac{1 \, \text{mol}}{342.30 \, \text{g}} = 0.045 \text{mol} \]
06

Calculate Volume in Liters for Sucrose Solution

Convert the given volume from milliliters to liters:\[ 74.0 \, \text{mL} = 0.0740 \, \text{L} \]
07

Calculate Molarity of Sucrose Solution

Substitute the values into the molarity formula:\[ M = \frac{0.045 \, \text{mol}}{0.0740 \, \text{L}} \approx 0.608 \, \text{M} \]
08

Calculate Moles of Sodium Chloride

First, calculate the molar mass of sodium chloride \((\text{NaCl})\). It is calculated as:\[ 22.99 + 35.45 = 58.44 \text{ g/mol} \]Now, calculate moles of sodium chloride by dividing the given mass by the molar mass:\[ 9.00 \, \text{g} \times \frac{1 \, \text{mol}}{58.44 \, \text{g}} = 0.154 \, \text{mol} \]
09

Calculate Volume in Liters for Sodium Chloride Solution

Convert the given volume from milliliters to liters:\[ 86.4 \, \text{mL} = 0.0864 \, \text{L} \]
10

Calculate Molarity of Sodium Chloride Solution

Substitute the values into the molarity formula:\[ M = \frac{0.154 \, \text{mol}}{0.0864 \, \text{L}} \approx 1.78 \, \text{M} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity Calculation
Molarity is a crucial concept in chemistry that helps us understand the concentration of a solution. It's defined as the number of moles of solute present in one liter of solution. The formula we use is:
  • \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
To perform a molarity calculation, follow these steps:1. Calculate the moles of solute using its mass and molar mass.2. Convert the solution's volume from milliliters to liters.3. Substitute these values into the molarity formula.
Remember, understanding molarity helps predict how a solution will behave in chemical reactions.
Mole Concept
The mole is a fundamental concept in chemistry. It serves as a bridge between the atomic scale and the laboratory scale. A mole represents \(6.022 \times 10^{23}\) particles, commonly atoms or molecules, and is defined by Avogadro's number.
This mole concept allows us to convert between a quantity in grams and the number of atoms or molecules in that quantity. The key is understanding molar mass, which is the mass of one mole of a substance measured in grams per mole (g/mol).
  • For example, the molar mass of water (H\(_2\)O) is calculated by adding twice the atomic mass of hydrogen and once the atomic mass of oxygen.
  • This makes the conversion straightforward between mass and moles.
Conversion of Units
In chemistry, converting units is essential, especially when dealing with solutions. We often need to convert volumes from milliliters (mL) to liters (L), required for molarity calculations.
  • To convert from mL to L, divide the number of milliliters by 1000, as there are 1000 milliliters in a liter.
Converting units also includes mass. For instance:
  • Grams to moles conversion requires dividing by the molar mass, as seen in many calculations involving molecular compounds.
Understanding these conversions helps ensure accurate solutions and reliable results in experiments.

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