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Chapter 4: Problem 36

How would you prepare \(1.00 \mathrm{~L}\) of a \(0.50-M\) solution of each of the following? a. \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from "concentrated" ( \(18 \mathrm{M}\) ) sulfuric acid b. HCl from "concentrated" (12 \(M\) ) reagent c. \(\mathrm{NiCl}_{2}\) from the salt \(\mathrm{NiCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) d. HNO \(_{3}\) from "concentrated" ( \(16 M\) ) reagent e. Sodium carbonate from the pure solid

Short Answer

Expert verified
To prepare 1.00 L of 0.50 M solutions: a. Measure 27.8 mL of 18 M H₂SO₄ and dilute with water to 1.00 L. b. Measure 41.7 mL of 12 M HCl and dilute with water to 1.00 L. c. Dissolve 118.85 g of NiCl₂·6H₂O in water to reach 1.00 L. d. Measure 31.3 mL of 16 M HNO₃ and dilute with water to 1.00 L. e. Dissolve 52.995 g of sodium carbonate in water to reach 1.00 L.

Step by step solution

01

Identify the initial and final concentrations and volumes

We are given the initial concentration (\(M_1\)) of the concentrated sulfuric acid as 18 M, and the desired final concentration (\(M_2\)) as 0.50 M. The final volume (\(V_2\)) should be 1.00 L.
02

Apply the dilution formula

Using the dilution formula, \(M_1V_1 = M_2V_2\), we can find the initial volume (\(V_1\)) required to prepare the final solution. \(V_1 = \frac{M_2V_2}{M_1} = \frac{(0.50\,\text{M})(1.00\,\text{L})}{18\,\text{M}} = 0.0278\,\text{L}\)
03

Calculate and perform the dilution

We need to measure 0.0278 L (27.8 mL) of concentrated sulfuric acid and dilute it with enough water to reach a final volume of 1.00 L. #b. Preparing 1.00 L of 0.50 M HCl from 12 M Concentrated Reagent#
04

Identify the initial and final concentrations and volumes

The initial concentration (\(M_1\)) of the concentrated HCl solution is 12 M, and the desired final concentration (\(M_2\)) is 0.50 M. The final volume (\(V_2\)) should be 1.00 L.
05

Apply the dilution formula

Using the dilution formula, \(M_1V_1 = M_2V_2\), we can find the initial volume (\(V_1\)) required to prepare the final solution. \(V_1 = \frac{M_2V_2}{M_1} = \frac{(0.50\,\text{M})(1.00\,\text{L})}{12\,\text{M}} = 0.0417\,\text{L}\)
06

Calculate and perform the dilution

We need to measure 0.0417 L (41.7 mL) of concentrated HCl and dilute it with enough water to reach a final volume of 1.00 L. #c. Preparing 1.00 L of 0.50 M NiCl₂ from NiCl₂·6H₂O salt#
07

Calculate the moles of solute needed

To prepare the final solution, we need to find the moles of NiCl₂ needed using the formula \(n =MV\). Here, n is the number of moles, M is the molarity (0.50 M), and V is the volume (1.00 L). \(n = (0.50\,\text{M})(1.00\,\text{L}) = 0.50\,\text{mol}\)
08

Convert moles to mass using molar mass

We will now convert moles of NiCl₂·6H₂O to mass using the molar mass of the compound, which is approximately 237.69 g/mol. \(m = n \cdot \text{MM} = (0.50\,\text{mol})(237.69\,\text{g/mol}) = 118.85\,\text{g}\)
09

Dissolve the salt in water

Weigh 118.85 g of NiCl₂·6H₂O and dissolve it in enough water to reach a final volume of 1.00 L. #d. Preparing 1.00 L of 0.50 M HNO₃ from 16 M Concentrated Reagent#
10

Identify the initial and final concentrations and volumes

The initial concentration (\(M_1\)) of the concentrated HNO₃ solution is 16 M, and the desired final concentration (\(M_2\)) is 0.50 M. The final volume (\(V_2\)) should be 1.00 L.
11

Apply the dilution formula

Using the dilution formula, \(M_1V_1 = M_2V_2\), we can find the initial volume (\(V_1\)) required to prepare the final solution. \(V_1 = \frac{M_2V_2}{M_1} = \frac{(0.50\,\text{M})(1.00\,\text{L})}{16\,\text{M}} = 0.0313\,\text{L}\)
12

Calculate and perform the dilution

We need to measure 0.0313 L (31.3 mL) of concentrated HNO₃ and dilute it with enough water to reach a final volume of 1.00 L. #e. Preparing 1.00 L of 0.50 M Sodium Carbonate from the Pure Solid#
13

Calculate the moles of solute needed

To prepare the final solution, we need to find the moles of sodium carbonate needed using the formula \(n =MV\). Here, n is the number of moles, M is the molarity (0.50 M), and V is the volume (1.00 L). \(n = (0.50\,\text{M})(1.00\,\text{L}) = 0.50\,\text{mol}\)
14

Convert moles to mass using molar mass

We will now convert moles of sodium carbonate to mass using the molar mass of the compound, which is approximately 105.99 g/mol. \(m = n \cdot \text{MM} = (0.50\,\text{mol})(105.99\,\text{g/mol}) = 52.995\,\text{g}\)
15

Dissolve the salt in water

Weigh 52.995 g of sodium carbonate and dissolve it in enough water to reach a final volume of 1.00 L.

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Most popular questions from this chapter

Many oxidation-reduction reactions can be balanced by inspection. Try to balance the following reactions by inspection. In each reaction, identify the substance reduced and the substance oxidized. a. \(\mathrm{Al}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2}(g)\) b. \(\mathrm{CH}_{4}(g)+\mathrm{S}(s) \rightarrow \mathrm{CS}_{2}(l)+\mathrm{H}_{2} \mathrm{~S}(g)\) c. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) d. \(\mathrm{Cu}(s)+\mathrm{Ag}^{+}(a q) \rightarrow \mathrm{Ag}(s)+\mathrm{Cu}^{2+}(a q)\)

A \(10.00-\mathrm{mL}\) sample of sulfuric acid from an automobile battery requires \(35.08 \mathrm{~mL}\) of \(2.12 M\) sodium hydroxide solution for complete neutralization. What is the molarity of the sulfuric acid? Sulfuric acid contains two acidic hydrogens.

Write net ionic equations for the reaction, if any, that occurs when aqueous solutions of the following are mixed. a. ammonium sulfate and barium nitrate b. lead(II) nitrate and sodium chloride c. sodium phosphate and potassium nitrate d. sodium bromide and rubidium chloride e. copper(II) chloride and sodium hydroxide

Calculate the concentration of all ions present in each of the following solutions of strong electrolytes. a. \(0.0200\) mole of sodium phosphate in \(10.0 \mathrm{~mL}\) of solution b. \(0.300\) mole of barium nitrate in \(600.0 \mathrm{~mL}\) of solution c. \(1.00 \mathrm{~g}\) of potassium chloride in \(0.500 \mathrm{~L}\) of solution d. \(132 \mathrm{~g}\) of ammonium sulfate in \(1.50 \mathrm{~L}\) of solution

Write the balanced formula, complete ionic, and net ionic equations for each of the following acid-base reactions. a. \(\mathrm{HNO}_{3}(a q)+\mathrm{Al}(\mathrm{OH})_{3}(s) \rightarrow\) b. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)+\mathrm{KOH}(a q) \rightarrow\) c. \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{HCl}(a q) \rightarrow\)
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