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Chapter 4: Problem 81

Some metal halides react with water to produce the metal oxide and the appropriate hydrogen halide (see photo). For example, $$ \mathrm{TiCl}_{4}(\ell)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{TiO}_{2}(\mathrm{s})+4 \mathrm{HCl}(\mathrm{g}) $$ (IMAGE CANNOT COPY) (a) Name the four compounds involved in this reaction. (b) If you begin with \(14.0 \mathrm{mL}\) of \(\mathrm{TiCl}_{4}(d=1.73 \mathrm{g} / \mathrm{mL})\) what mass of water, in grams, is required for complete reaction? (c) What mass of each product is expected?

Short Answer

Expert verified
(a) Titanium(IV) chloride, water, titanium dioxide, hydrogen chloride. (b) 4.60 g of water needed. (c) 10.20 g of \(\mathrm{TiO}_2\) and 18.63 g of \(\mathrm{HCl}\) produced.

Step by step solution

01

Naming the Compounds

Identify and name the compounds in the reaction \( \mathrm{TiCl}_{4}(\ell) + 2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{TiO}_{2}(\mathrm{s}) + 4 \mathrm{HCl}(\mathrm{g}) \). The four compounds are: \( \mathrm{TiCl}_{4} \) is Titanium(IV) chloride, \( \mathrm{H}_{2} \mathrm{O} \) is water, \( \mathrm{TiO}_{2} \) is titanium dioxide, and \( \mathrm{HCl} \) is hydrogen chloride.
02

Calculate Moles of \(\mathrm{TiCl}_{4}\)

Start by finding the mass of \( \mathrm{TiCl}_{4} \) using its volume and density. \( \text{Mass} = 14.0 \text{ mL} \times 1.73 \text{ g/mL} = 24.22 \text{ g} \). Then, calculate the moles of \( \mathrm{TiCl}_{4} \) using its molar mass \( (189.71 \text{ g/mol}) \). Moles of \( \mathrm{TiCl}_{4} = \frac{24.22}{189.71} \approx 0.1277 \text{ moles} \).
03

Determine Mass of Water Required

According to the balanced equation, 2 moles of water are required per mole of \( \mathrm{TiCl}_{4} \). Therefore, the water moles needed are \( 2 \times 0.1277 = 0.2554 \text{ moles} \). Use the molar mass of water \( (18.02 \text{ g/mol}) \) to find the mass: \( \text{Mass of water} = 0.2554 \times 18.02 \approx 4.60 \text{ g} \).
04

Calculate Mass of Titanium Dioxide Produced

From the reaction, 1 mole of \( \mathrm{TiCl}_{4} \) produces 1 mole of \( \mathrm{TiO}_{2} \). Thus, the moles of \( \mathrm{TiO}_{2} \) are the same as \( \mathrm{TiCl}_{4} \): \( 0.1277 \text{ moles} \). The molar mass of \( \mathrm{TiO}_{2} \) is \( 79.87 \text{ g/mol} \), so the mass is \( 0.1277 \times 79.87 \approx 10.20 \text{ g} \).
05

Calculate Mass of Hydrogen Chloride Produced

The reaction indicates that 1 mole of \( \mathrm{TiCl}_{4} \) produces 4 moles of \( \mathrm{HCl} \). Therefore, \( 0.1277 \times 4 = 0.5108 \text{ moles of } \mathrm{HCl} \). The molar mass of \( \mathrm{HCl} \) is \( 36.46 \text{ g/mol} \), so the mass is \( 0.5108 \times 36.46 \approx 18.63 \text{ g} \).

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Key Concepts

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

Chemical Reactions
Chemical reactions are processes where reactants transform into products. They are characterized by the rearrangement of atoms. In the reaction provided, we see titanium(IV) chloride \( \text{TiCl}_4 \) reacting with water \( \text{H}_2\text{O} \) to form titanium dioxide \( \text{TiO}_2 \) and hydrogen chloride \( \text{HCl} \).
This is a typical example of a substitution reaction where one element or group in a molecule is replaced by another. The equation describing this process is already balanced, indicating that reactants and products contain equal numbers of each type of atom.
To fully understand this reaction, it's essential to recognize the type of chemical transformation occurring. It simplifies predicting similar reactions with different compounds.
Stoichiometry
Stoichiometry is a branch of chemistry focusing on the quantitative relationships in chemical reactions. It helps predict the amount of products formed from given reactants.
In the example with titanium(IV) chloride, stoichiometry allows us to determine how much water is needed to react with a given amount of \( \text{TiCl}_4 \), as well as the mass of products \( \text{TiO}_2 \) and \( \text{HCl} \) formed.
  • First, convert given quantities (like volume or mass) to moles using density and molar mass.
  • Use stoichiometric coefficients from the balanced chemical equation to relate moles of different substances.
  • Finally, convert moles back to mass if needed, using molar masses.
These steps ensure precise calculations of substances involved in chemical reactions.
Titanium Dioxide
Titanium dioxide \( \text{TiO}_2 \) is a white solid used widely in paints, sunscreens, and food coloring due to its excellent opacity and brightness properties. It's also a crucial product in this chemical reaction.
Titanium dioxide forms as a result of titanium(IV) chloride reacting with water. Its solid nature implies that it can be collected as a precipitate in the reaction medium.
The role of \( \text{TiO}_2 \) here also illustrates its chemical stability, a reason it's regularly used in various applications. Understanding the production and utility of \( \text{TiO}_2 \) helps grasp its significance in both industrial and chemical contexts.
Hydrogen Chloride
Hydrogen chloride \( \text{HCl} \) is a gas at room temperature. However, when dissolved in water, it is known as hydrochloric acid, widely used in industrial and laboratory settings.
During the given chemical reaction, hydrogen chloride is a gaseous product formed alongside titanium dioxide. The molecular formation of \( \text{HCl} \) indicates a synthesis reaction occurring simultaneously during the substitution reformation with water.
The significance of \( \text{HCl} \) in reactions like this extends to its application in manufacturing, metal pickling, and even pH regulation in solutions. Understanding the production of \( \text{HCl} \) contributes to a deeper insight into the diverse applications of this important chemical compound.

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Most popular questions from this chapter

Spectrophotometry A solution of a dye was analyzed by spectrophotometry, and the following calibration data were collected. $$\begin{array}{cc} \text { Dye Concentration } & \text { Absorbance }(A) \text { at } 475 \mathrm{nm} \\ \hline 0.50 \times 10^{-6} \mathrm{M} & 0.24 \\ 1.5 \times 10^{-6} \mathrm{M} & 0.36 \\ 2.5 \times 10^{-6} \mathrm{M} & 0.44 \\ 3.5 \times 10^{-6} \mathrm{M} & 0.59 \\ 4.5 \times 10^{-6} \mathrm{M} & 0.70 \\ \hline \end{array}$$ (a) Construct a calibration plot, and determine the slope and intercept. (b) What is the dye concentration in a solution with \(A=0.52 ?\)

A Phosphate in urine can be determined by spectrophotometry. After removing protein from the sample, it is treated with a molybdenum compound to give, ultimately, a deep blue polymolybdate. The absorbance of the blue polymolybdate can be measured at \(650 \mathrm{nm}\) and is directly related to the urine phosphate concentration. A 24 -hour urine sample was collected from a patient; the volume of urine was 1122 mL. The phosphate in a \(1.00 \mathrm{mL}\), portion of the urine sample was converted to the blue polymolybdate and diluted to \(50.00 \mathrm{mL} .\) A calibration curve was prepared using phosphate-containing solutions. (Concentrations are reported in grams of phosphorus (P) per liter of solution.) $$\begin{array}{lc} \text { Solution (mass P/L) } & \begin{array}{c} \text { Absorbance at } 650 \mathrm{nm} \\ \text { in a } 1.0-\mathrm{cm} \text { cell } \end{array} \\ \hline 1.00 \times 10^{-6} \mathrm{g} & 0.230 \\ 2.00 \times 10^{-6} \mathrm{g} & 0.436 \\ 3.00 \times 10^{-6} \mathrm{g} & 0.638 \\ 4.00 \times 10^{-6} \mathrm{g} & 0.848 \\ \text { Urine sample } & 0.518 \\ \hline \end{array}$$ (a) What are the slope and intercept of the calibration curve? (b) What is the mass of phosphorus per liter of urine? (c) What mass of phosphate did the patient excrete in the one-day period?

A Calcium and magnesium carbonates occur together in the mineral dolomite. Suppose you heat a sample of the mineral to obtain the oxides, \(\mathrm{CaO}\) and \(\mathrm{MgO},\) and then treat the oxide sample with hydrochloric acid. If \(7.695 \mathrm{g}\) of the oxide sample requires 125 mL. of 2.55 M \(\mathrm{HCl}\). $$ \begin{aligned} \mathrm{CaO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \rightarrow \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \\ \mathrm{MgO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$ what is the weight percent of each oxide (CaO and \(\mathrm{MgO})\) in the sample?

A You need to know the volume of water in a small swimming pool, but, owing to the pool's irregular shape, it is not a simple matter to determine its dimensions and calculate the volume. To solve the problem, you stir in a solution of a dye \((1.0 \mathrm{g}\) of methylene blue, \(\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{ClN}_{3} \mathrm{S},\) in \(50.0 \mathrm{mL}\) of water). After the dye has mixed with the water in the pool, you take a sample of the water. Using a spectrophotometer, you determine that the concentration of the dye in the pool is \(4.1 \times 10^{-8} \mathrm{M} .\) What is the volume of water in the pool?

Make the following conversions. In each case, tell whether the solution is acidic or basic. \(\mathbf{p} \mathbf{H}$$\quad$$\left[\mathbf{H}_{3} \mathbf{O}^{*}\right]\) (a) 1.00\(\quad\)______ (b) 10.50\(\quad\)______ (c) ______\(\quad1.3 \times 10^{-3} \mathrm{M}\) (d) ______\(\quad2.3 \times 10^{-8} \mathrm{M}\)
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