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Chapter 11: Problem 9

SIMPLEST OR EMPIRICAL FORMULAS II-9. Calcium carbide produces acetylene when water is added to it. The acetylene evolved is burned to provide the light source on spelunkers' helmets. Chemical analysis shows that calcium carbide is \(62.5 \%\) (by mass) calcium and \(37.5 \%\) (by mass) carbon. Determine the empirical formula of calcium carbide.

Short Answer

Expert verified
The empirical formula of calcium carbide is \( \text{CaC}_2 \).

Step by step solution

01

Convert Percentages to Masses

Assume you have 100 grams of calcium carbide. This means you have 62.5 grams of calcium and 37.5 grams of carbon.
02

Convert Masses to Moles for Calcium

To find the moles of calcium, use the molar mass of calcium, which is approximately 40.08 g/mol. Calculate the moles by dividing the mass by the molar mass: \( \frac{62.5\, \text{g}}{40.08\, \text{g/mol}} \approx 1.56\, \text{mol} \).
03

Convert Masses to Moles for Carbon

To find the moles of carbon, use the molar mass of carbon, which is 12.01 g/mol. Calculate the moles by dividing the mass by the molar mass: \( \frac{37.5\, \text{g}}{12.01\, \text{g/mol}} \approx 3.12\, \text{mol} \).
04

Determine the Simplest Ratio

Divide the moles of each element by the smallest number of moles calculated in the previous steps to find the simplest whole number ratio: \( \frac{1.56}{1.56} = 1 \) for calcium and \( \frac{3.12}{1.56} = 2 \) for carbon.
05

Write the Empirical Formula

The simplest whole number ratio of calcium to carbon in calcium carbide is 1:2. Thus, the empirical formula is \( \text{CaC}_2 \).

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Key Concepts

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

calcium carbide
Calcium carbide is a fascinating compound used in various applications, including the production of acetylene gas. This compound is crucial for its role in creating light for spelunkers' helmets, where the gas produced is burned to provide illumination.
Calcium carbide is synthesized from calcium oxide and carbon. When water is added to calcium carbide, it undergoes a chemical reaction producing acetylene gas (C2H2) and calcium hydroxide. This property makes it highly valued in industries that require portable light sources.
  • The molecular structure consists of one calcium atom and two carbon atoms.
  • It is primarily used in generating acetylene for illumination and as a reagent in chemical synthesis.
  • It's a solid compound with crystalline appearance.
Understanding its composition and how it reacts with water is essential for its safe and effective application.
percent composition
Percent composition refers to the percentage by mass of each element within a compound. It is an essential concept used in chemistry to determine the empirical formula of a compound.
To calculate percent composition, assume a 100 g sample, helping convert percentages directly into grams. This creates a straightforward calculation path, simplifying the conversion from masses to moles.
  • For calcium carbide, the analysis indicates 62.5% calcium and 37.5% carbon by mass.
  • Percent composition helps infer an element's presence relative to the whole compound.
  • This concept is crucial for determining both empirical and molecular formulas.
By understanding these percentages, chemists can determine the simplest ratio of elements in a compound.
moles to empirical formula
Converting moles to an empirical formula is a key step in determining the simplest whole-number ratio of elements within a compound. This involves a few straightforward calculations.
Once you've calculated the moles for each element using their respective molar masses, the next step is to divide each mole value by the smallest mole value obtained for any element in the compound. This step simplifies finding the simplest ratio and results in the empirical formula.
  • This process starts with converting mass into moles using the formula: moles = mass/molar mass.
  • Then, compare the mole values by dividing them by the smallest mole value.
  • Adjust for any non-entire numbers by multiplying all ratios by the same factor to achieve whole numbers.
This method universally applies to any compound, ensuring accurate determination of the empirical formula.
chemical analysis
Chemical analysis is the study used to determine the precise composition of a substance. It involves quantifying the elements or compounds present in a sample and is vital for understanding chemical reactions and formulations.
In determining the empirical formula, chemical analysis gives the percent composition data that acts as the foundation for finding the exact elementary ratios.
  • Combining theoretical knowledge with practical experimentation aids in deriving compound formulas.
  • This analysis is pivotal in developing new chemical compounds and materials.
  • It integrates numerous techniques like chromatography and spectroscopy to separate and identify substances.
Essentially, chemical analysis provides the data needed to conclude the empirical formula, ensuring precision in chemical formulation and experimentation.

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Most popular questions from this chapter

Combustion analysis of a \(1.000\) -gram sample of a compound known to contain only carbon, hydrogen, and oxygen produces \(1.500\) grams of \(\mathrm{CO}_{2}(g)\) and \(0.409\) grams of \(\mathrm{H}_{2} \mathrm{O}(g)\). Determine the empirical formula of the compound.

Nickel sulfate forms a blue-green hydrate with the formula \(\mathrm{NiSO}_{4} \cdot n \mathrm{H}_{2} \mathrm{O}(s) .\) If this hydrate is heated to a high enough temperature, \(\mathrm{H}_{2} \mathrm{O}(g)\) can be driven off, leaving the greenish-yellow anhydrous salt \(\mathrm{NiSO}_{4}(s)\). A \(12.060\) -gram sample of the hydrate was heated to \(300^{\circ} \mathrm{C}\). The resulting \(\mathrm{NiSO}_{4}(s)\) had a mass of \(7.101\) grams. Calculate the value of \(n\) in \(\mathrm{NiSO}_{4} \cdot n \mathrm{H}_{2} \mathrm{O}(s)\)

When left exposed to air and water, iron metal will rust, forming an oxide. If a bar of pure iron is allowed to rust and then both the rust and remaining iron are weighed, will the total mass be greater than, less than, or equal to the mass of the original iron bar? If all the rust is scraped off, will the mass of the bar now be greater than, less than, or equal to the original mass of the bar? Justify your answers.

MOLECULAR FORMULAS The chemical 2-propanone, commonly known as acetone, is an important chemical solvent; a familiar home use is as a nail polish remover. Chemical analysis shows that acetone is \(62.0 \%\) carbon, \(10.4 \%\) hydrogen, and \(27.5 \%\) oxygen by mass. Determine the empirical formula of acetone. In a separate experiment, the molecular mass is found to be \(58.1 .\) What is the molecular formula of acetone?

Solution containing \(12.5\) grams of silver nitrate is added to a solution containing \(67.2\) grams of sodium sulfate. (a) Write the balanced chemical equation for this reaction. (b) Determine how many grams of solid silver sulfate are formed after the reaction comes to completion. (c) How many grams of the reactant in excess will remain after the reaction?
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