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Chapter 11: Problem 6

Calculate the mass percentage of each element in each of the following compounds to four significant figures. (a) methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l)\) (b) water, \(\mathrm{H}_{2} \mathrm{O}(l)\)

Short Answer

Expert verified
Methanol: C: 37.48%, H: 12.58%, O: 49.94%. Water: H: 11.19%, O: 88.81%.

Step by step solution

01

Find the Molar Mass of Methanol

Methanol has the formula \( \text{CH}_3\text{OH} \). To find the molar mass, we add the molar masses of each element: - Carbon (C): 1 atom \( \times 12.01 \text{ g/mol} = 12.01 \text{ g/mol} \)- Hydrogen (H): 4 atoms \( \times 1.008 \text{ g/mol} = 4.032 \text{ g/mol} \)- Oxygen (O): 1 atom \( \times 16.00 \text{ g/mol} = 16.00 \text{ g/mol} \)The total molar mass is \( 12.01 + 4.032 + 16.00 = 32.042 \text{ g/mol} \).
02

Calculate Mass Percentage of Each Element in Methanol

To find the mass percentage, divide the mass of each element by the total molar mass and multiply by 100.- Carbon: \( \frac{12.01}{32.042} \times 100 \approx 37.48\% \)- Hydrogen: \( \frac{4.032}{32.042} \times 100 \approx 12.58\% \)- Oxygen: \( \frac{16.00}{32.042} \times 100 \approx 49.94\% \)
03

Find the Molar Mass of Water

Water has the formula \( \text{H}_2\text{O} \). The molar masses are:- Hydrogen (H): 2 atoms \( \times 1.008 \text{ g/mol} = 2.016 \text{ g/mol} \)- Oxygen (O): 1 atom \( \times 16.00 \text{ g/mol} = 16.00 \text{ g/mol} \)The total molar mass is \( 2.016 + 16.00 = 18.016 \text{ g/mol} \).
04

Calculate Mass Percentage of Each Element in Water

To calculate the mass percentage, divide each element's mass by the total mass and multiply by 100.- Hydrogen: \( \frac{2.016}{18.016} \times 100 \approx 11.19\% \)- Oxygen: \( \frac{16.00}{18.016} \times 100 \approx 88.81\% \)

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Key Concepts

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

Molar Mass Calculation
Understanding how to calculate molar mass is a fundamental skill in chemistry. It helps you figure out the total mass of a compound based on individual elements. Molar mass is essentially the sum of the masses of all atoms in a molecule.
To illustrate, let's consider methanol with the chemical formula \( \text{CH}_3\text{OH} \).
  • Carbon (C) has a molar mass of 12.01 g/mol.
  • Hydrogen (H) has a molar mass of 1.008 g/mol. Since there are four hydrogen atoms in methanol, you multiply 1.008 by 4, resulting in 4.032 g/mol.
  • Oxygen (O) contributes 16.00 g/mol.
Add these masses: \( 12.01 + 4.032 + 16.00 = 32.042 \text{ g/mol} \).
This gives the total molar mass of methanol. The same principle applies to other compounds like water \( \text{H}_2\text{O} \), where you sum up the contributions of hydrogen and oxygen to get 18.016 g/mol.

Key Points:

Remember that accurately knowing molar masses is crucial for subsequent calculations like mass percentage.
Elemental Composition
Elemental composition refers to the proportion of each element within a compound. It's crucial for understanding how different elements combine to form a molecule. Let's take a closer look using methanol and water.
  • In methanol \( \text{CH}_3\text{OH} \), its composition consists of carbon, hydrogen, and oxygen.
  • For water \( \text{H}_2\text{O} \), the composition is simpler; it's just hydrogen and oxygen.
Each compound has a specific arrangement and number of each type of atom, which defines its elemental composition. Calculating the mass percentage of these elements reveals how much each element contributes to the compound's total weight.
This percentage breakdown helps in understanding the role and proportion of each element within the compound.

Practical Application:

Knowledge of elemental composition is not only academic but also useful in real-world applications like pharmaceuticals, where precise element ratios are vital.
Chemical Formula Analysis
Analyzing a chemical formula gives insight into the structure and proportions within a molecule. It assists in determining molecular characteristics and behaviors.
For example, the chemical formula \( \text{CH}_3\text{OH} \) tells us that methanol contains:
  • one carbon atom (C)
  • four hydrogen atoms (H)
  • one oxygen atom (O)
Understanding these numbers is vital because they determine the physical and chemical properties of the compound. A formula like \( \text{H}_2\text{O} \) is even more straightforward, clearly indicating two hydrogens bonded to one oxygen.
By quantifying these elements and understanding their arrangement, scientists can predict reactions, structure, and function.

Benefits:

Analyzing chemical formulas helps in fields such as synthetic chemistry, biology for metabolic pathway mapping, and environmental science for tracking pollutants.

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Most popular questions from this chapter

PERCENTAGE YIELD II-59. Titanium dioxide is converted to titanium tetrachloride by reaction with chlorine gas and carbon according to the equation $$ \mathrm{TiO}_{2}(s)+2 \mathrm{Cl}_{2}(g)+2 \mathrm{C}(s) \rightarrow \mathrm{TiCl}_{4}(g)+2 \mathrm{CO}(g) $$ Suppose \(50.0\) grams of \(\mathrm{TiO}_{2}(s)\) are reacted with excess \(\mathrm{Cl}_{2}(g)\) and \(\mathrm{C}(s)\), and \(55.0\) grams of \(\mathrm{TiCl}_{4}(g)\) are obtained. Calculate the percentage yield of \(\mathrm{TiCl}_{4}(g)\).

A \(3.78\) -gram sample of iron metal is reacted with sulfur to produce \(5.95\) grams of iron sulfide. Determine the empirical formula of this compound.

A \(5.00\) -gram sample of aluminum metal is burned in an oxygen atmosphere to produce \(9.45\) grams of aluminum oxide. Use these data to determine the empirical formula of aluminum oxide.

The concept of determining which reactant is limiting and which is in excess is akin to determining the number of sandwiches that can be made from a set number of ingredients. Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of cheese sandwiches that can be prepared from a loaf of 24 slices of bread and a package of 40 slices of cheese. Which of the two ingredients limits the number of sandwiches that can be made? What quantity of the ingredient in excess remains?

MIXTURES II - 43. Table salt, \(\mathrm{NaCl}(s)\), and sugar, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\), are accidentally mixed. A \(5.00\) -gram sample is burned, and \(2.20\) grams of \(\mathrm{CO}_{2}(g)\) are produced. What is the mass percentage of the table salt in the mixture?
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