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Chapter 13: Problem 39

Calculate the molarity of the following aqueous solutions: (a) \(0.540 \mathrm{~g} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) in \(250.0 \mathrm{~mL}\) of solution, (b) \(22.4 \mathrm{~g} \mathrm{LiClO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) in \(125 \mathrm{~mL}\) of solution, (c) \(25.0 \mathrm{~mL}\) of \(3.50 \mathrm{M} \mathrm{HNO}_{3}\) diluted to \(0.250 \mathrm{~L}\).

Short Answer

Expert verified
For part (a), the molarity of the Mg(NO鈧)鈧 solution is 0.0146 M. For part (b), the molarity of the LiClO鈧劼3H鈧侽 solution is 1.06 M. For part (c), the final molarity of the HNO鈧 solution after dilution is 0.350 M.

Step by step solution

01

Calculate moles of solute (Mg(NO鈧)鈧) for part (a)

First, we need to determine the molar mass of Mg(NO鈧)鈧. Using the periodic table, we find the molar masses of the elements: Mg = 24.31 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol. Mg(NO鈧)鈧 = 1*Mg + 2*(1*N + 3*O) = 1*24.31 + 2*(14.01 + 3*16.00) = 148.33 g/mol Now, we can convert the mass of Mg(NO鈧)鈧 given (0.540 g) to moles: moles of Mg(NO鈧)鈧 = mass/molar mass = 0.540 g / 148.33 g/mol = 0.00364 mol
02

Calculate the molarity (M) for part (a)

We are given the volume of the solution (250.0 mL) which needs to be converted to liters: volume = 250.0 mL * (1 L / 1000 mL) = 0.250 L Now, we can calculate the molarity by dividing the mol of solute by the liters of solution: M = moles/volume = 0.00364 mol / 0.250 L = 0.0146 M For part (a), the molarity of the Mg(NO鈧)鈧 solution is 0.0146 M.
03

Calculate moles of solute (LiClO鈧劼3H鈧侽) for part (b)

First, we need to determine the molar mass of LiClO鈧劼3H鈧侽. Li = 6.94 g/mol, Cl = 35.45 g/mol, O = 16.00 g/mol, H = 1.01 g/mol LiClO鈧劼3H鈧侽 = Li + Cl + 4*O + 3*(2*H + O) = 6.94 + 35.45 + 4*16.00 + 3*(2*1.01 + 16.00) = 167.84 g/mol Now, we can convert the mass of LiClO鈧劼3H鈧侽 given (22.4 g) to moles: moles of LiClO鈧劼3H鈧侽 = mass/molar mass = 22.4 g / 167.84 g/mol = 0.133 mol
04

Calculate the molarity (M) for part (b)

We are given the volume of the solution (125 mL) which needs to be converted to liters: volume = 125 mL * (1 L / 1000 mL) = 0.125 L Now, we can calculate the molarity by dividing the mol of solute by the liters of solution: M = moles/volume = 0.133 mol / 0.125 L = 1.06 M For part (b), the molarity of the LiClO鈧劼3H鈧侽 solution is 1.06 M.
05

Calculate the final molarity for part (c)

Given the molarity (3.50 M) and volume (25.0 mL) of the concentrated HNO鈧 solution, we can use the dilution equation: M鈧乂鈧 = M鈧俈鈧 where M鈧 is the initial molarity, V鈧 is the initial volume, M鈧 is the final molarity, and V鈧 is the final volume. Here, M鈧 = 3.50 M, V鈧 = 25.0 mL, V鈧 = 0.250 L, and we need to find M鈧. First, we need to convert V鈧 to liters: V鈧 = 25.0 mL * (1 L / 1000 mL) = 0.0250 L Now, we can solve the equation for M鈧: M鈧 = M鈧乂鈧 / V鈧 = (3.50 M * 0.0250 L) / 0.250 L = 0.350 M For part (c), the final molarity of the HNO鈧 solution after dilution is 0.350 M.

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Key Concepts

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

Molar Mass
Molar mass is the mass of one mole of a given substance, measured in grams per mole (g/mol). It is the sum of the atomic masses of all the atoms in a molecule, and it is a vital concept when we are trying to convert between mass and moles of a substance, just like in our textbook exercises above.

To calculate the molar mass, we look up the atomic masses of each element on the periodic table and multiply them by the number of atoms of that element in the formula. In our first example, for Mg(NO鈧)鈧, the calculation involves adding together the atomic masses of magnesium, nitrogen, and oxygen in the proportions that they appear in the compound.
Moles of Solute
The term 'moles of solute' refers to the amount of solute in moles that is dissolved in a given amount of solution. Chemists use the concept of 'the mole' to count atoms, ions, or molecules. One mole contains Avogadro's number of entities, which is approximately 6.022 x 10虏鲁.

To find the moles of a solute, we divide the mass of the solute by its molar mass. As shown in the solutions provided, for the solution of LiClO鈧劼3H鈧侽, you first calculate its molar mass and then use the given mass to find the number of moles. Understanding the conversion between mass and moles is crucial in chemistry, especially when preparing solutions of a desired concentration.
Dilution Equation
When the concentration of a solution is adjusted by adding solvent, this is known as dilution. The dilution equation, an indispensable tool for this process, is represented as M鈧乂鈧 = M鈧俈鈧. This equation states that the product of the initial molarity (M鈧) and the initial volume (V鈧) equals the product of the final molarity (M鈧) and the final volume (V鈧).

It is especially useful when you are trying to determine the concentration of a solution after dilution, like we did in part (c) of our exercise. This equation assumes that the amount of solute remains constant; only the volume and concentration change due to the addition of more solvent.
Solution Concentration
Solution concentration is expressed in various ways, with molarity being one of the most common, especially in aqueous solutions. Molarity (M) is defined as the number of moles of solute per liter of solution. It is critical for expressing how concentrated or dilute a solution is, which is vital for reactions and experiments in chemistry.

In the examples given, the molarity of the solutions is calculated by dividing the moles of solute by the volume of the solution in liters. This method allows chemists to know precisely how much solute is present in a specific volume of solution, which is essential for precise scientific measurements and reactions.

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Most popular questions from this chapter

At \(63.5^{\circ} \mathrm{C}\) the vapor pressure of \(\mathrm{H}_{2} \mathrm{O}\) is 175 torr, and that of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is 400 torr. A solution is made by mixing equal masses of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). (a) What is the mole fraction of ethanol in the solution? (b) Assuming ideal- solution behavior, what is the vapor pressure of the solution at \(63.5^{\circ} \mathrm{C} ?\) (c) What is the mole fraction of ethanol in the vapor above the solution?

A solution contains \(0.115 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) and an unknown number of moles of sodium chloride. The vapor pressure of the solution at \(30^{\circ} \mathrm{C}\) is \(25.7\) torr. The vapor pressure of pure water at this temperature is \(31.8\) torr. Calculate the number of moles of sodium chloride in the solution. (Hint: remember that sodium chloride is a strong electrolyte.)

Explain how each of the following factors helps determine the stability or instability of a colloidal dispersion: (a) particulate mass, (b) hydrophobic character, (c) charges on colloidal particles.

(a) A sample of hydrogen gas is generated in a closed container by reacting \(2.050 \mathrm{~g}\) of zinc metal with \(15.0 \mathrm{~mL}\) of \(1.00 \mathrm{M}\) sulfuric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete. (b) The volume over the solution is \(122 \mathrm{~mL}\). Calculate the partial pressure of the hydrogen gas in this volume at \(25^{\circ} \mathrm{C}\), ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at \(25^{\circ} \mathrm{C}\) is \(7.8 \times 10^{-4} \mathrm{~mol} / \mathrm{L}-\mathrm{atm} .\) Estimate the number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)?

(a) What is an ideal solution? (b) The vapor pressure of pure water at \(60^{\circ} \mathrm{C}\) is 149 torr. The vapor pressure of water over a solution at \(60^{\circ} \mathrm{C}\) containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law? Explain.
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