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A 2.634 -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 g. What was the mass percent of \(\mathrm{CuCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) in the original sample?

Short Answer

Expert verified
The mass percent of \(\mathrm{CuCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) is approximately 91.6%.

Step by step solution

01

Determine the mass of water lost

Start by finding the mass of the water that was driven off. This can be calculated by subtracting the mass of the sample after heating from the mass before heating. \[\text{Mass of water lost} = \text{Initial mass of sample} - \text{Final mass of sample} = 2.634\, \text{g} - 2.125\, \text{g} = 0.509\, \text{g}\]
02

Calculate moles of water lost

Next, calculate the moles of water that were lost. Use the molar mass of water, which is approximately 18.015 g/mol.\[\text{Moles of water lost} = \frac{0.509\, \text{g}}{18.015\, \text{g/mol}} \approx 0.0283\, \text{mol}\]
03

Relate moles of water to moles of cupric chloride dihydrate

Since each molecule of \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\) contains two water molecules, the moles of \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\) is half of the moles of water lost.\[0.0283\, \text{mol}\, \text{of } \mathrm{H}_2\mathrm{O} \to 0.01415\, \text{mol}\, \mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\]
04

Calculate the mass of pure cupric chloride dihydrate

Determine the mass of pure \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\) using its molar mass. The molar mass is approximately 170.48 g/mol.\[\text{Mass of } \mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O} = 0.01415\, \text{mol} \times 170.48\, \text{g/mol} \approx 2.413\, \text{g}\]
05

Calculate the mass percent of cupric chloride dihydrate in the sample

Finally, calculate the mass percent of \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\) in the original sample by dividing the mass of the pure substance by the initial mass of the sample and multiplying by 100.\[\text{Mass percent} = \left(\frac{2.413\, \text{g}}{2.634\, \text{g}}\right) \times 100 \approx 91.6\%\]

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Key Concepts

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

Mass Percent Calculation
Mass percent is an important concept in chemical analysis. It helps us understand the composition of a sample by comparing different components within it. In simple terms, mass percent indicates how much of each component is present relative to the total mass of the mixture.
To find the mass percent of a substance, you need two pieces of information:
  • The mass of the component you are interested in.
  • The total mass of the sample.
The formula for mass percent is:\[\text{Mass Percent} = \left( \frac{\text{Mass of component}}{\text{Total mass of sample}} \right) \times 100\]This calculation allows chemists and scientists to evaluate the purity or concentration of substances in a mixture. It's a crucial step in determining how much of a compound is present in an experiment or a commercial product.
Molar Mass
Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It's usually expressed in grams per mole (g/mol). Molar mass links the macroscopic properties of a substance to its microscopic structure, allowing scientists to convert between mass and number of particles.
To calculate the molar mass:
  • Find the atomic masses of each element in the compound from the periodic table.
  • Multiply the atomic mass by the number of atoms of that element in the formula.
  • Add up all these values to get the molar mass of the compound.
For example, the molar mass of a water molecule (\(\mathrm{H}_{2}\mathrm{O}\)) is approximately 18.015 g/mol, calculated as follows:
  • Hydrogen: 2 atoms × 1.008 g/mol = 2.016 g/mol
  • Oxygen: 1 atom × 16.00 g/mol = 16.00 g/mol
  • Total: 2.016 g/mol + 16.00 g/mol = 18.015 g/mol
Understanding molar mass is essential for converting mass to moles, which is a common step in stoichiometry and chemical reactions.
Cupric Chloride Dihydrate
Cupric chloride dihydrate is a chemical compound with the formula \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\). It's made up of copper, chlorine, and water molecules, and is commonly used in various chemical processes, including electroplating and as a fungicide.
This compound is interesting because it contains water molecules as part of its structure, which is known as hydration. The copper ions in the compound give it a characteristic blue-green color when dissolved in water.
  • Cupric (Copper (II) ion) — the cupric part indicates copper is in its +2 oxidation state.
  • Chloride — the chloride ions are part of the salt formed with copper.
  • Dihydrate — signifies that there are two water molecules associated with each formula unit of the compound.
Understanding cupric chloride dihydrate involves knowing how these molecules interact and how they can be manipulated in chemical reactions, especially regarding their water content.
Water of Hydration
Water of hydration refers to water molecules that are chemically bonded within a crystalline structure of a compound. These molecules are integral to the structure of hydrates, affecting their physical properties and how they react in chemical processes.
The concept of water of hydration is significant in studying compounds like \(\mathrm{CuCl}_{2}\cdot2\mathrm{H}_{2}\mathrm{O}\), where the water molecules are included in the crystal lattice. When heated, hydrates lose their water of hydration, which can be measured as a change in mass, helping identify and determine their hydrated state.
The process of losing water from a hydrate upon heating is called dehydration. During this process:
  • The structure of the crystalline compound changes.
  • The compound typically changes color, indicating a phase change.
  • The remaining substance, known as an anhydrous compound, has a different mass and properties.
Understanding how water of hydration affects hydrates is crucial in industries where controlling moisture content is important, such as food processing and pharmaceuticals.

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Most popular questions from this chapter

In the photographic developing process, silver bromide is dissolved by adding sodium thiosulfate. $$\operatorname{AgBr}(s)+2 \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(\mathrm{aq}) \rightarrow \mathrm{Na}_{3} \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}(\mathrm{aq})+\mathrm{NaBr}(\mathrm{aq})$$ If you want to dissolve 0.225 g of AgBr, what volume of \(0.0138 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3},\) in milliliters, should be used?

Antacids are chemical compounds that can give immediate relief from indigestion or heartburn because they contain carbonate or hydroxide ions that neutralize stomach acids. Some common active ingredients include \(\mathrm{NaHCO}_{3}, \mathrm{KHCO}_{3}\), \(\mathrm{CaCO}_{3}, \mathrm{Mg}(\mathrm{OH})_{2},\) and \(\mathrm{Al}(\mathrm{OH})_{3} .\) Although these compounds give quick relief, they are not recommended for prolonged consumption. Calcium carbonate may contribute to the growth of kidney stones, and calcium carbonate and aluminum hydroxide may cause constipation. Magnesium hydroxide, on the other hand, is a mild laxative that can cause diarrhea. Antacids containing magnesium, therefore, are often combined with aluminum hydroxide since the aluminum counteracts the laxative properties of the magnesium. (a) Which of the compounds listed above produce gas-forming reactions when combined with HCl? (b) One tablet of Tums Regular Strength Antacid contains \(500 . \mathrm{mg} \mathrm{CaCO}_{3}\) . (i) Write a balanced chemical equation for the reaction of \(\mathrm{CaCO}_{3}\) and stomach acid \((\mathrm{HCl})\) (ii) What volume (in mL) of 0.500 \(\mathrm{M}\) HCl(aq) will react completely with one tablet of Tums? (c) The active ingredients in Rolaids are \(\mathrm{CaCO}_{3}\) and \(\mathrm{Mg}(\mathrm{OH})_{2}\). (i) Write a balanced chemical equation for the reaction of \(\mathrm{Mg}(\mathrm{OH})_{2}\) and \(\mathrm{HCl}\). (ii) If \(29.52 \mathrm{mL}\) of \(0.500 \mathrm{M} \mathrm{HCl}\) is required to titrate one tablet of Rolaids and the tablet contains \(550 \mathrm{mg}\) of \(\mathrm{CaCO}_{3},\) what mass of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is present in one tablet? (d) Maalox may be purchased in either a liquid or solid form. One teaspoon of the liquid form of Maalox" contains a mixture of \(200 . \mathrm{mg}\) of \(\mathrm{Al}(\mathrm{OH})_{3}\) and \(200 . \mathrm{mg}\) of \(\mathrm{Mg}(\mathrm{OH})_{2} .\) What volume of 0.500 \(\mathrm{M} \mathrm{HCl}(\mathrm{aq})\) will react completely with one teaspoon of Maalox \(^{\pi / 2} ?\) (e) Which product neutralizes the greatest amount of acid when taken in the quantities presented above: one tablet of Tums" or Rolaids" or one teaspoon of Maalox"?

In an experiment, 1.056 g of a metal carbonate, containing an unknown metal \(\mathrm{M},\) is heated to give the metal oxide and \(0.376 \mathrm{g} \mathrm{CO}_{2}\). $$\mathrm{MCO}_{3}(\mathrm{s})+\text { heat } \rightarrow \mathrm{MO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ What is the identity of the metal \(\mathrm{M}\) ? (a) \(\mathrm{M}=\mathrm{Ni}\) (b) \(\mathrm{M}=\mathrm{Cu}\) (c) \(\mathrm{M}=\mathrm{Zn}\) (d) \(\mathrm{M}=\mathrm{Ba}\)

The reaction of \(750 .\) g each of \(\mathrm{NH}_{3}\) and \(\mathrm{O}_{2}\) was found to produce \(562 \text { g of } \mathrm{NO} \text { (see pages } 177-179)\). $$4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\ell)$$ (a) What mass of water is produced by this reaction? (b) What mass of \(\mathrm{O}_{2}\) is required to consume \(750 . \mathrm{g}\) of \(\mathrm{NH}_{3} ?\)

Two beakers sit on a balance; the total mass is \(167.170 \mathrm{g} .\) One beaker contains a solution of \(\mathrm{KI}\) the other contains a solution of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} .\) When the solution in one beaker is poured completely into the other, the following reaction occurs: $$2 \mathrm{KI}(\mathrm{aq})+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{KNO}_{3}(\mathrm{aq})+\mathrm{PbI}_{2}(\mathrm{s})$$ What is the total mass of the beakers and solutions after reaction? Explain completely.

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