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Chapter 4: Problem 89

Silicon and hydrogen form a series of compounds with the general formula \(\mathrm{Si}_{x} \mathrm{H}_{y}\). To find the formula of one of them, a 6.22 -g sample of the compound is burned in oxygen. All of the Si is converted to \(11.64 \mathrm{g}\) of \(\mathrm{SiO}_{2},\) and all of the H is converted to \(6.980 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula of the silicon compound?

Short Answer

Expert verified
The empirical formula is \(\text{SiH}_4\).

Step by step solution

01

Calculate Moles of SiO2

The molecular weight of SiO2 is calculated as follows: \( \text{Si: } 28.0855 \, \text{g/mol, O: } 16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol} \). Thus, the molar mass of SiO2 is \( 28.0855 + 32.00 = 60.0855 \, \text{g/mol} \). To find the moles of SiO2 formed, divide the mass of SiO2 by its molar mass: \( \frac{11.64 \, \text{g}}{60.0855 \, \text{g/mol}} \approx 0.1937 \, \text{mol} \).
02

Find Moles of Si in SiO2

In one mole of SiO2, there is one mole of Si. Therefore, the moles of Si are the same as moles of SiO2, which is approximately \(0.1937 \, \text{mol} \).
03

Calculate Moles of H2O

The molecular weight of H2O is \( \text{H: } 1.008 \, \text{g/mol} \times 2 = 2.016 \, \text{g/mol + O: } 16.00 \, \text{g/mol} = 18.016 \, \text{g/mol} \). To find the moles of H2O, use: \( \frac{6.980 \, \text{g}}{18.016 \, \text{g/mol}} \approx 0.3875 \, \text{mol} \).
04

Determine Moles of H in H2O

Each mole of H2O contains 2 moles of H. Therefore, the moles of H are \(0.3875 \, \text{mol} \times 2 = 0.775 \, \text{mol} \).
05

Ratio of Moles of Si to H

The ratio of moles of Si to moles of H can be expressed as \( \frac{0.1937}{0.1937} : \frac{0.775}{0.1937} \), which simplifies to 1:4. This indicates the compound is composed of one silicon atom for every four hydrogen atoms.
06

Empirical Formula

The empirical formula of the compound is determined by using the simplest ratio of Si to H. From Step 5, the empirical formula is \(\text{SiH}_4\).

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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 chemical substances transform into new substances through the breaking and forming of bonds. In the given exercise, the chemical reaction involves burning a compound of silicon and hydrogen in oxygen.
This reaction converts all silicon to silicon dioxide ( SiO_{2} ) and all hydrogen to water ( H_{2}O ).
These transformations are typical examples of chemical reactions where substances combine or rearrange to form new products.
Some key aspects of chemical reactions include:
  • Reactants and Products: Reactants are the starting materials that undergo change, while products are the substances formed by the reaction.
  • Conservation of Mass: In a chemical reaction, the total mass of reactants is equal to the total mass of the products. This principle is crucial for understanding the stoichiometry of a reaction.
  • Energy Changes: Chemical reactions often involve energy changes, with energy absorbed to break bonds and released when new bonds form.
Understanding the basic nature of such reactions helps in determining the empirical formula, as seen in extracting information from the mass of reactants and products.
Molecular Weight
Molecular weight, also known as molecular mass, is the sum of the atomic weights of all atoms in a molecule.
It is expressed in atomic mass units (amu) or grams per mole (g/mol). Calculating molecular weight is a foundational concept for determining the number of moles of substances involved in chemical reactions.
In the problem presented, molecular weights played a crucial role. The molecular weights of SiO_{2} and H_{2}O were calculated as follows:
  • For SiO2: Molecular weight is the sum of one Si (28.0855 g/mol) and two O atoms (16.00 g/mol each), totaling 60.0855 g/mol.
  • For H2O: The molecular weight combines two H atoms (1.008 g/mol each) and one O atom (16.00 g/mol), resulting in 18.016 g/mol.
These weights were used to convert masses into moles, a pivotal step in the determination of the empirical formula, allowing for the calculation of moles based on provided product masses.
Stoichiometry
Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the balanced equations representing chemical reactions.
Stoichiometry calculations rely on the concept of moles, providing a means to predict the amounts of products formed or reactants required.
Key Steps in Stoichiometric Calculations:
  • Identifying the Data: Determine the masses or quantities of reactants and products.
  • Convert Masses to Moles: Use molecular weights to change grams to moles as shown in the exercise: 11.64 g of SiO2 corresponds to approximately 0.1937 moles, and 6.980 g of H2O corresponds to approximately 0.3875 moles.
  • Relate Substances by Mole Ratios: The exercise reveals a ratio of moles of Si to H of 1:4, indicating the composition of the compound as SiH4.
The simplest ratio derived from stoichiometric calculations is often the empirical formula.
It provides insight into the basic composition of a compound, as demonstrated by the task of computing the empirical formula of silicon hydride.

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Most popular questions from this chapter

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"?

Titanium(IV) oxide, \(\mathrm{TiO}_{2}\), is heated in hydrogen gas to give water and a new titanium oxide, \(\mathrm{Ti}_{x} \mathrm{O}_{y},\) If \(1.598 \mathrm{g}\) of \(\mathrm{TiO}_{2}\) produces \(1.438 \mathrm{g}\) of \(\mathrm{Ti}_{x} \mathrm{O}_{y},\) what is the empirical formula of the new oxide?

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?

An unknown compound has the formula \(\mathrm{C}_{x} \mathrm{H}_{y} \mathrm{O}_{z}\) You burn 0.0956 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 \(62.1 \mathrm{g} / \mathrm{mol},\) what is the molecular formula?

To find the formula of a compound composed of iron and carbon monoxide, \(\mathrm{Fe}_{x}(\mathrm{CO})_{y^{\prime}}\) the compound is burned in pure oxygen to give \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(\mathrm{CO}_{2} .\) If you burn \(1.959 \mathrm{g}\) of \(\mathrm{Fe}_{x}(\mathrm{CO})_{y}\) and obtain \(0.799 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(2.200 \mathrm{g}\) of \(\mathrm{CO}_{2},\) what is the empirical formula of \(\mathrm{Fe}_{x}(\mathrm{CO})_{y} ?\)
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