Textbook Question
A solution is made containing 20.8 g of phenol (C6H5OH) in 425 g of ethanol (CH3CH2OH). Calculate (a) the mole fraction of phenol,
Ch.13 - Properties of Solutions
Chapter 13, Problem 43a,b
Calculate the molarity of the following aqueous solutions: (a) 0.540 g of Mg(NO3)2 in 250.0 mL of solution, (b) 22.4 g of LiClO4 • 3 H2O in 125 mL of solution,
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Step 1: Understand the concept of molarity. Molarity (M) is defined as the number of moles of solute per liter of solution. The formula to calculate molarity is: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
Step 2: Calculate the molarity for part (a). First, determine the molar mass of \( \text{Mg(NO}_3\text{)}_2 \). The molar mass is the sum of the atomic masses of all atoms in the formula: \( \text{Mg} = 24.31 \text{g/mol}, \text{N} = 14.01 \text{g/mol}, \text{O} = 16.00 \text{g/mol} \). Calculate the molar mass of \( \text{Mg(NO}_3\text{)}_2 \).
Step 3: Convert the mass of \( \text{Mg(NO}_3\text{)}_2 \) to moles using its molar mass. Use the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).
Step 4: Convert the volume of the solution from milliliters to liters for part (a). Remember that 1 L = 1000 mL, so divide the volume in milliliters by 1000.
Step 5: Calculate the molarity for part (b) using a similar approach. First, determine the molar mass of \( \text{LiClO}_4 \cdot 3 \text{H}_2\text{O} \) by adding the atomic masses of \( \text{Li} = 6.94 \text{g/mol}, \text{Cl} = 35.45 \text{g/mol}, \text{O} = 16.00 \text{g/mol}, \text{H} = 1.01 \text{g/mol} \). Then, convert the mass to moles and the volume to liters, and finally calculate the molarity using the formula \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molarity
Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how much solute is present in a given volume of solution. To calculate molarity, one must first determine the number of moles of the solute using its molar mass and then divide by the volume of the solution in liters.
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Molarity
Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule. Knowing the molar mass is essential for converting grams of a substance to moles, which is a necessary step in calculating molarity.
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Volume Conversion
Volume conversion is the process of converting units of volume, such as milliliters (mL) to liters (L). Since molarity is defined in terms of liters, it is important to convert the volume of the solution from mL to L by dividing by 1000. This ensures that the calculations for molarity are accurate and consistent with the standard units used in chemistry.
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Related Practice
Textbook Question
A solution is made containing 20.8 g of phenol (C6H5OH) in 425 g of ethanol (CH3CH2OH). Calculate (c) the molality of phenol.
Textbook Question
Calculate the molarity of the following aqueous solutions: (c) 25.0 mL of 3.50 M HNO3 diluted to 0.250 L.
Textbook Question
What is the molarity of each of the following solutions: (b) 5.25 g of Mn(NO3)2⋅2H2O in 175 mL of solution,
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Textbook Question
What is the molarity of each of the following solutions: (c) 35.0 mL of 9.00 M H2SO4 diluted to 0.500 L?