Describe how you would prepare each of the following aqueous solutions, starting with solid KBr: (a) \(0.75 \mathrm{~L}\) of \(1.5 \times 10^{-2} M \mathrm{KBr},\) (b) \(125 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KBr},\) (c) \(1.85 \mathrm{~L}\) of a solution that is \(12.0 \% \mathrm{KBr}\) by mass (the density of the solution is \(1.10 \mathrm{~g} / \mathrm{mL}\) ), (d) a \(0.150 \mathrm{M}\) solution of \(\mathrm{KBr}\) that contains just enough KBr to precipitate \(16.0 \mathrm{~g}\) of AgBr from a solution containing \(0.480 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}\)

Short Answer

Expert verified
(a) Calculate moles of KBr needed: moles of KBr = (1.5 × 10⁻² M) * (0.75 L). Convert moles to grams: mass of KBr = (moles of KBr) * (119 g/mol). Preparation: Weigh out the mass of KBr, dissolve in a 0.75 L volumetric flask, and fill with water. (b) Calculate molality: mass of solvent = (125 g) / (0.180 m). Calculate moles of KBr: moles of KBr = (0.180 m) * (mass of solvent in kg). Convert moles to grams: mass of KBr = (moles of KBr) * (119 g/mol). Preparation: Weigh out the mass of KBr, dissolve in the calculated mass of the solvent. (c) Calculate mass of KBr: mass of KBr = 0.12 * (1.10 g/mL) * (1.85 L * 1000 mL/L). Preparation: Weigh out the mass of KBr, dissolve in a 1.85 L volumetric flask, and fill with water. (d) Determine moles of AgBr: moles of AgBr = (16.0 g) / (187.8 g/mol). Calculate moles of KBr (equal to moles of AgBr). Convert moles to grams: mass of KBr = (moles of KBr) * (119 g/mol). Find volume: volume = moles of KBr / (0.150 M). Preparation: Weigh out the mass of KBr, dissolve in a volumetric flask of the calculated volume, and fill with water.

Step by step solution

01

(a) Calculate the moles of KBr needed for the solution

As we are given the volume (0.75 L) and molarity(1.5 * 10^-2 M) of the desired solution, first, find out the number of moles of KBr required: moles of KBr = Molarity * Volume = (1.5 × 10⁻² M) * (0.75 L)
02

(a) Convert moles to grams

Now that we have the number of moles required, we need to convert this to grams using the molar mass of KBr (molecular weight = 39.1 g/mol for K + 79.9 g/mol for Br = 119 g/mol): mass of KBr = (moles of KBr) * (molar mass of KBr)
03

(a) Preparation of the solution

Finally, weigh out the calculated mass of KBr and dissolve it in a 0.75 L volumetric flask. Fill the flask with water (preferably distilled water) up to the 0.75 L mark to make the 1.5 * 10^-2 M KBr solution.
04

(b) Calculate molality of KBr solution

We are given the mass (125 g) and molality (0.180 m) of the desired solution. First, divide the mass by the molality to find the mass of the solvent (usually water in an aqueous solution): mass of solvent = mass of solution / molality = (125 g) / (0.180 m)
05

(b) Calculate the moles of KBr required

Now that we have the mass of the solvent, we can find the number of moles of KBr required: moles of KBr = (molality) * (mass of solvent in kg)
06

(b) Convert moles to grams

Next, convert the number of moles of KBr to grams using the molar mass of KBr (119 g/mol): mass of KBr = (moles of KBr) * (molar mass of KBr)
07

(b) Preparation of the solution

Weigh out the calculated mass of KBr and dissolve it in the calculated mass of the solvent (usually distilled water) to prepare the 0.180 m KBr solution.
08

(c) Calculate the mass of KBr required

As we are given the volume (1.85 L), mass fraction (12.0 %), and density (1.10 g/mL) of the desired solution, first, find out the mass of KBr required: mass of KBr = mass fraction * density * volume = 0.12 * (1.10 g/mL) * (1.85 L * 1000 mL/L)
09

(c) Preparation of the solution

Finally, weigh out the calculated mass of KBr and dissolve it in a 1.85 L volumetric flask. Fill the flask with water (preferably distilled water) up to the 1.85 L mark to make the 12.0% KBr solution.
10

(d) Determine moles of AgBr

We are given the mass of precipitated AgBr (16.0 g) and the number of moles of AgNO3 (0.480 mol). First, calculate the moles of AgBr using its molar mass (molecular weight = 107.9 g/mol for Ag + 79.9 g/mol for Br = 187.8 g/mol): moles of AgBr = (mass of AgBr) / (molar mass of AgBr)
11

(d) Calculate the moles of KBr required

Since the reaction between KBr and AgNO3 is 1:1, the number of moles of KBr required is equal to the number of moles of AgBr.
12

(d) Convert moles to grams

Next, convert the number of moles of KBr to grams using the molar mass of KBr (119 g/mol): mass of KBr = (moles of KBr) * (molar mass of KBr)
13

(d) Find the volume of the solution

The concentration of the KBr solution is given as 0.150 M. Calculate the volume of the solution using the relationship between moles, molarity, and volume: volume = moles of KBr / (0.150 M)
14

(d) Preparation of the solution

Finally, weigh out the calculated mass of KBr and dissolve it in a volumetric flask of the calculated volume. Fill the flask with water (preferably distilled water) up to the mark to make the desired 0.150 M KBr solution. This solution contains just enough KBr to precipitate 16.0 g of AgBr from a solution containing 0.480 mol of AgNO3.

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