Chapter 4

Mass Relationships in Chemical Reactions: Basic Stoichiometry Aluminum reacts with oxygen to give aluminum oxide. $$ 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}) $$ What amount of \(\mathrm{O}_{2},\) in moles, is needed for complete reaction with 6.0 mol of Al? What mass of \(\mathrm{Al}_{2} \mathrm{O}_{3},\) in grams, can be produced?

What mass of HCl, in grams, is required to react with \(0.750 \mathrm{g}\) of \(\mathrm{Al}(\mathrm{OH})_{3} ?\) What mass of water, in grams, is produced? $$ \mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})+3 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$

Like many metals, aluminum reacts with a halogen to give a metal halide ( 4 Figure 2.12 ). $$ 2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Br}_{2}(\ell) \rightarrow \mathrm{Al}_{2} \mathrm{Br}_{6}(\mathrm{s}) $$ What mass of \(\mathrm{Br}_{2}\), in grams, is required for complete reaction with \(2.56 \mathrm{g}\) of Al? What mass of white, solid \(\mathrm{Al}_{2} \mathrm{Br}_{6}\) is expected?

The balanced equation for the reduction of iron ore to the metal using CO is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g}) $$ (a) What is the maximum mass of iron, in grams, that can be obtained from \(454 \mathrm{g}(1.00 \mathrm{lb})\) of iron(III) oxide? (b) What mass of \(\mathrm{CO}\) is required to react with \(454 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3} ?\)

Methane, \(\mathrm{CH}_{4},\) burns in oxygen. (a) What are the products of the reaction? (b) Write the balanced equation for the reaction. (c) What mass of \(\mathrm{O}_{2}\), in grams, is required for complete combustion of \(25.5 \mathrm{g}\) of methane? (d) What is the total mass of products expected from the combustion of \(25.5 \mathrm{g}\) of methane?

The formation of water-insoluble silver chloride is useful in the analysis of chloride-containing substances. Consider the following unbalanced equation: \(\mathrm{BaCl}_{2}(\mathrm{aq})+\mathrm{AgNO}_{3}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s})+\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) (a) Write the balanced equation. (b) What mass of \(\mathrm{AgNO}_{3},\) in grams, is required for complete reaction with \(0.156 \mathrm{g}\) of \(\mathrm{BaCl}_{2} ?\) What mass of AgCl is produced?

For each question below, set up an amounts table that lists the initial amount or amounts of reactants, the changes in amounts of reactants and products, and the amounts of reactants and products after reaction (see page 159 and Example \(4 . \overline{1}\) ). The metals industry was a major source of air pollution years ago. One common process involved "roasting" metal sulfides in the air: $$ 2 \mathrm{PbS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{PbO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{g}) $$ If 2.50 mol of PbS is heated in air, what amount of \(\mathrm{O}_{2}\) is required for complete reaction? What amounts of PbO and \(\mathrm{SO}_{2}\) are expected?

Iron ore is converted to iron metal in a reaction with carbon. $$ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g}) $$ If 6.2 mol of \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\) is used, what amount of \(\mathrm{C}(\mathrm{s})\) is needed, and what amounts of Fe and \(\mathrm{CO}_{2}\) are produced?

Chromium metal reacts with oxygen to give chromium(III) oxide, \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) (a) Write a balanced equation for the reaction. (b) What mass (in grams) of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) is produced if \(0.175 \mathrm{g}\) of chromium metal is converted completely to the oxide? (c) What mass of \(\mathrm{O}_{2}\) (in grams) is required for the reaction?

Ethane, \(\mathrm{C}_{2} \mathrm{H}_{6},\) burns in oxygen. (a) What are the products of the reaction? (b) Write the balanced equation for the reaction. (c) What mass of \(\mathrm{O}_{2}\), in grams, is required for complete combustion of 13.6 of ethane? (d) What is the total mass of products expected from the combustion of \(13.6 \mathrm{g}\) of ethane?

Limiting Reactants Sodium sulfide, \(\mathrm{Na}_{2} \mathrm{S}\), is used in the leather industry to remove hair from hides. The \(\mathrm{Na}_{2} \mathrm{S}\) is made by the reaction $$ \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{s})+4 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{S}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) $$ Suppose you mix \(15 \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and \(7.5 \mathrm{g}\) of \(\mathrm{C}\). Which is the limiting reactant? What mass of \(\mathrm{Na}_{2} \mathrm{S}\) is produced?

Ammonia gas can be prepared by the reaction of a metal oxide such as calcium oxide with ammonium chloride. \(\mathrm{CaO}(\mathrm{s})+2 \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) \rightarrow\) $$ 2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CaCl}_{2}(\mathrm{s}) $$ If \(112 \mathrm{g}\) of \(\mathrm{CaO}\) and \(224 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{Cl}\) are mixed, what is the limiting reactant, and what mass of \(\mathrm{NH}_{3}\) can be produced?

The compound \(\mathrm{SF}_{6}\) is made by burning sulfur in an atmosphere of fluorine. The balanced equation is $$ \mathrm{S}_{\mathrm{s}}(\mathrm{s})+24 \mathrm{F}_{2}(\mathrm{g}) \rightarrow 8 \mathrm{SF}_{6}(\mathrm{g}) $$ If you begin with 1.6 mol of sulfur, \(\mathrm{S}_{\mathrm{s}},\) and 35 mol of \(\mathrm{F}_{2}\) which is the limiting reagent?

Disulfur dichloride, \(\mathrm{S}_{2} \mathrm{Cl}_{2}\), is used to vulcanize rubber. It can be made by treating molten sulfur with gaseous chlorine: $$ \mathrm{S}_{\mathrm{s}}(\ell)+4 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{S}_{2} \mathrm{Cl}_{2}(\ell) $$ Starting with a mixture of \(32.0 \mathrm{g}\) of sulfur and \(71.0 \mathrm{g}\) of \(\mathrm{Cl}_{2}\) (a) Which is the limiting reactant? (b) What is the theoretical yield of \(\mathrm{S}_{2} \mathrm{Cl}_{2} ?\) (c) What mass of the excess reactant remains when the reaction is completed?

The reaction of methane and water is one way to prepare hydrogen for use as a fuel: $$ \mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) $$ If you begin with \(995 \mathrm{g}\) of \(\mathrm{CH}_{4}\) and \(2510 \mathrm{g}\) of water, (a) Which reactant is the limiting reactant? (b) What is the maximum mass of \(\mathrm{H}_{2}\) that can be prepared? (c) What mass of the excess reactant remains when the reaction is completed?

Aluminum chloride, AlCl \(_{3}\), is made by treating scrap aluminum with chlorine. $$ 2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{AlCl}_{3}(\mathrm{s}) $$ If you begin with \(2.70 \mathrm{g}\) of \(\mathrm{Al}\) and \(4.05 \mathrm{g}\) of \(\mathrm{Cl}_{2}\) (a) Which reactant is limiting? (b) What mass of AlC \(_{3}\) can be produced? (c) What mass of the excess reactant remains when the reaction is completed? (d) Set up an amounts table for this problem.

Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) burns in air \(\left(\mathrm{O}_{2}\right)\) to give \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) (a) Write a balanced equation for the reaction. (b) If \(215 \mathrm{g}\) of \(\mathrm{C}_{6} \mathrm{H}_{14}\) is mixed with \(215 \mathrm{g}\) of \(\mathrm{O}_{2}\), what masses of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are produced in the reaction? (c) What mass of the excess reactant remains after the hexane has been burned? (d) Set up an amounts table for this problem.

A You mix 25.0 mL of 0.234 M FeC 1 , with 42.5 mL of \(0.453 \mathrm{M} \mathrm{NaOH}\) (a) What mass of \(\mathrm{Fe}(\mathrm{OH})_{3}\) (in grams) will precipitate from this reaction mixture? (b) One of the reactants \(\left(\mathrm{FeCl}_{3} \text { or } \mathrm{NaOH}\) ) is present \right. in a stoichiometric excess. What is the molar concentration of the excess reactant remaining in solution after \(\mathrm{Fe}(\mathrm{OH})\), has been precipitated?

Ammonia gas can be prepared by the following reaction: \(\mathrm{CaO}(\mathrm{s})+2 \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) \rightarrow\) $$ 2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CaCl}_{2}(\mathrm{s}) $$ If \(112 \mathrm{g}\) of \(\mathrm{CaO}\) and \(224 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{Cl}\) are mixed, the theoretical yield of \(\mathrm{NH}_{3}\) is \(68.0 \mathrm{g}\) (Study Question 12 ). If only \(16.3 \mathrm{g}\) of \(\mathrm{NH}_{3}\) is actually obtained, what is its percent yield?

The deep blue compound \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4}\) is made by the reaction of copper(II) sulfate and ammonia. $$ \mathrm{CuSO}_{4}(\mathrm{aq})+4 \mathrm{NH}_{3}(\mathrm{aq}) \rightarrow \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4}(\mathrm{aq}) $$ (a) If you use \(10.0 \mathrm{g}\) of \(\mathrm{CuSO}_{4}\) and excess \(\mathrm{NH}_{3}\), what is the theoretical yield of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} ?\) (b) If you isolate \(12.6 \mathrm{g}\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4},\) what is the percent yield of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} ?\)

Black smokers are found in the depths of the oceans (page 110 ). Thinking that the conditions in these smokers might be conducive to the formation of organic compounds, two chemists in Germany found the following reaction could occur in similar conditions. $$ 2 \mathrm{CH}_{3} \mathrm{SH}+\mathrm{CO} \rightarrow \mathrm{CH}_{3} \mathrm{COSCH}_{3}+\mathrm{H}_{2} \mathrm{S} $$ If you begin with \(10.0 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{SH}\) and excess \(\mathrm{CO}\) (a) What is the theoretical yield of \(\mathrm{CH}_{3} \mathrm{COSCH}_{3} ?\) (b) If \(8.65 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{COSCH}_{3}\) is isolated, what is its percent yield?

Analysis of Mixtures A mixture of \(\mathrm{CuSO}_{4}\) and \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has a mass of 1.245 g. After heating to drive off all the water, the mass is only \(0.832 \mathrm{g} .\) What is the mass percent of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture? (See page \(95 .\) )

A \(2.634-\mathrm{g}\) sample containing impure \(\mathrm{CuCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) was heated. The sample mass after heating to drive off the water was \(2.125 \mathrm{g} .\) What was the mass percent of \(\mathrm{CuCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) in the original sample?

A sample of limestone and other soil materials was heated, and the limestone decomposed to give calcium oxide and carbon dioxide. $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ A \(1.506-\mathrm{g}\) sample of limestone-containing material gave \(0.558 \mathrm{g}\) of \(\mathrm{CO}_{2},\) in addition to \(\mathrm{CaO},\) after being heated at a high temperature. What was the mass percent of \(\mathrm{CaCO}_{3}\) in the original sample?

At higher temperatures, NaHCO is converted quantitatively to \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) $$ 2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ Heating a \(1.7184-\mathrm{g}\) sample of impure NaHCO \(_{3}\) gives \(0.196 \mathrm{g}\) of \(\mathrm{CO}_{2} .\) What was the mass percent of \(\mathrm{NaHCO}_{3}\) in the original 1.7184 -g sample?

A pesticide contains thallium(I) sulfate, \(\mathrm{TI}_{2} \mathrm{SO}_{4}\). Dissolving a \(10.20-\mathrm{g}\) sample of impure pesticide in water and adding sodium iodide precipitates \(0.1964 \mathrm{g}\) of thallium(I) iodide, TII. $$ \mathrm{TI}_{2} \mathrm{SO}_{4}(\mathrm{aq})+2 \mathrm{NaI}(\mathrm{aq}) \rightarrow 2 \mathrm{TII}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq}) $$ What is the mass percent of \(\mathrm{TI}_{2} \mathrm{SO}_{4}\) in the original \(10.20-\mathrm{g}\) sample?

A The aluminum in a \(0.764 \mathrm{g}\) sample of an unknown material was precipitated as aluminum hydroxide, \(\mathrm{Al}(\mathrm{OH})_{3},\) which was then converted to \(\mathrm{Al}_{2} \mathrm{O}_{3}\) by heating strongly. If \(0.127 \mathrm{g}\) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) is obtained from the \(0.764-\mathrm{g}\) sample, what is the mass percent of aluminum in the sample?

Using Stoichiometry to Determine Empirical and Molecular Formulas Styrene, the building block of polystyrene, consists of only \(\mathrm{C}\) and \(\mathrm{H}\). If \(0.438 \mathrm{g}\) of styrene is burned in oxygen and produces \(1.481 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.303 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O},\) what is the empirical formula of styrene?

Mesitylene is a liquid hydrocarbon. Burning \(0.115 \mathrm{g}\) of the compound in oxygen gives \(0.379 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.1035 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of mesitylene?

Cyclopentane is a simple hydrocarbon. If \(0.0956 \mathrm{g}\) of the compound is burned in oxygen, \(0.300 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.123 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are isolated. (a) What is the empirical formula of cyclopentane? (b) If a separate experiment gave \(70.1 \mathrm{g} / \mathrm{mol}\) as the molar mass of the compound, what is its molecular formula?

Azulene is a beautiful blue hydrocarbon. If \(0.106 \mathrm{g}\) of the compound is burned in oxygen, \(0.364 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.0596 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are isolated. (a) What is the empirical formula of azulene? (b) If a separate experiment gave \(128.2 \mathrm{g} / \mathrm{mol}\) as the molar mass of the compound, what is its molecular formula?

An unknown compound has the formula \(\mathrm{C}_{x} \mathrm{H}_{2} \mathrm{O}_{2} .\) You burn \(0.0956 \mathrm{g}\) of the compound and isolate \(0.1356 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.0833 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound? If the molar mass is 62. I g/mol, what is the molecular formula?

An unknown compound has the formula \(\mathrm{C}_{x} \mathrm{H}, \mathrm{O}_{z} .\) You burn \(0.1523 \mathrm{g}\) of the compound and isolate \(0.3718 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.1522 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound? If the molar mass is \(72.1 \mathrm{g} / \mathrm{mol},\) what is the molecular formula?

Nickel forms a compound with carbon monoxide, \(\mathrm{Ni}_{x}(\mathrm{CO})_{\gamma}\). To determine its formula, you carefully heat a \(0.0973-\mathrm{g}\) sample in air to convert the nickel to \(0.0426 \mathrm{g}\) of \(\mathrm{NiO}\) and the \(\mathrm{CO}\) to \(0.100 \mathrm{g}\) of \(\mathrm{CO}_{2} .\) What is the empirical formula of \(\mathrm{Ni}_{x}(\mathrm{CO}), 2\)

Solution Concentration If \(6.73 \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is dissolved in enough water to make \(250 .\) mL of solution, what is the molar concentration of the sodium carbonate? What are the molar concentrations of the \(\mathrm{Na}^{+}\) and \(\mathrm{CO}_{3}^{2-}\) ions?

Some potassium dichromate \(\left(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\right), 2.335 \mathrm{g},\) is dissolved in enough water to make exactly \(500 .\) mL. of solution. What is the molar concentration of the potassium dichromate? What are the molar concentrations of the \(\mathrm{K}^{+}\) and \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) ions?

What is the mass of solute, in grams, in \(250 .\) mL. of a \(0.0125 \mathrm{M}\) solution of \(\mathrm{KMnO}_{4} ?\)

What is the mass of solute, in grams, in 125 mL. of a \(1.023 \times 10^{-3} \mathrm{M}\) solution of \(\mathrm{Na}_{3} \mathrm{PO}_{4} ?\) What is the molar concentration of the \(\mathrm{Na}^{+}\) and \(\mathrm{PO}_{4}^{3-}\) ion?

What volume of \(0.123 \mathrm{M} \mathrm{NaOH},\) in milliliters, contains \(25.0 \mathrm{g}\) of \(\mathrm{NaOH} ?\)

What volume of \(2.06 \mathrm{M} \mathrm{KMnO}_{4},\) in liters, contains \(322 \mathrm{g}\) of solute?

Identify the ions that exist in each aqueous solution, and specify the concentration of each ion. (a) \(0.25 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) (b) \(0.123 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) (c) \(0.056 \mathrm{M} \mathrm{HNO}_{3}\)

Identify the ions that exist in each aqueous solution, and specify the concentration of each ion. (a) \(0.12 \mathrm{M} \mathrm{BaCl}_{2}\) (b) \(0.0125 \mathrm{M} \mathrm{CuSO}_{4}\) (c) \(0.500 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\)

Preparing Solutions An experiment in your laboratory requires \(500 .\) mL. of a \(0.0200 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) You are given solid \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) distilled water, and a \(500 .\) -mL. volumetric flask. Describe how to prepare the required solution.

What mass of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) is required to prepare \(250 .\) mL of a solution that has a concentration of \(0.15 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} ?\)

If you dilute \(25.0 \mathrm{mL}\) of \(1.50 \mathrm{M}\) hydrochloric acid to \(500 . \mathrm{mL},\) what is the molar concentration of the dilute acid?

If \(4.00 \mathrm{mL}\) of \(0.0250 \mathrm{M} \mathrm{CuSO}_{4}\) is diluted to \(10.0 \mathrm{mL}\) with pure water, what is the molar concentration of copper(II) sulfate in the diluted solution?

Which of the following methods would you use to prepare \(1.00 \mathrm{L}\) of \(0.125 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} ?\) (a) Dilute \(20.8 \mathrm{mL}\) of \(6.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) to a volume of \(1.00 \mathrm{L}\) (b) Add \(950 .\) mL. of water to 50.0 mL of \(3.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\)

Which of the following methods would you use to prepare \(300 .\) mL. of \(0.500 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} ?\) (a) Add \(30.0 \mathrm{mL}\), of \(1.50 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) to \(270 .\) mL. of water. (b) Dilute \(250 .\) mL of \(0.600 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}\) to a volume of \(300 . \mathrm{mL}.\)

You have \(250 .\) mL of \(0.136 \mathrm{M}\) HCl. Using a volumetric pipet, you take \(25.00 \mathrm{mL}\) of that solution and dilute it to \(100.00 \mathrm{mL}\) in a volumetric flask. Now you take \(10.00 \mathrm{mL}\) of that solution, using a volumetric pipet, and dilute it to \(100.00 \mathrm{mL}\) in a volumetric flask. What is the concentration of hydrochloric acid in the final solution?

A Suppose you have \(100.00 \mathrm{mL}\) of a solution of a dye and transfer \(2.00 \mathrm{mL}\) of the solution to a \(100.00-\mathrm{mL}\) volumetric flask. After adding water to the \(100.00 \mathrm{mL}\) mark, you take 5.00 mL. of that solution and again dilute to \(100.00 \mathrm{mL}\). If you find the dye concentration in the final diluted sample is \(0.000158 \mathrm{M},\) what was the dye concentration in the original solution?