Ch.10 - Gases: Their Properties & Behavior

Problem 150

Chapter 10, Problem 150

Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO2 and 0.1838 g of H2O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g.(b) What is the molecular weight and molecular formula of methyl tert-butyl ether?

Verified step by step guidance

Determine the moles of CO2 and H2O produced in the combustion analysis. Use the molar mass of CO2 (44.01 g/mol) and H2O (18.02 g/mol) to convert the masses of CO2 and H2O to moles.

Calculate the moles of carbon and hydrogen in the original compound. Each mole of CO2 corresponds to one mole of carbon atoms, and each mole of H2O corresponds to two moles of hydrogen atoms.

Use the given mass of the original compound (0.1500 g) and the calculated moles of carbon and hydrogen to estimate the mass of oxygen in the compound by subtracting the mass of carbon and hydrogen from the total mass.

Convert the mass of oxygen to moles using the molar mass of oxygen (16.00 g/mol).

Use the ideal gas law (PV = nRT) to calculate the molar mass of the compound. Convert the temperature from Celsius to Kelvin, use the given pressure and volume, and solve for n (number of moles). Then, calculate the molecular weight by dividing the mass of the vapor (3.233 g) by the moles of vapor.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

10m

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Combustion Analysis

Combustion analysis is a technique used to determine the composition of organic compounds by burning them in excess oxygen. The products of combustion, typically carbon dioxide (CO2) and water (H2O), are measured to calculate the amounts of carbon and hydrogen in the original sample. This method is essential for deriving empirical formulas and ultimately helps in determining molecular weights.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for understanding the behavior of gases under various conditions and is used to calculate the number of moles of vapor present in the flask after the methyl tert-butyl ether is introduced. It allows for the conversion of mass measurements into moles, which is necessary for determining molecular weight.

Molecular Weight and Molecular Formula

Molecular weight is the sum of the atomic weights of all atoms in a molecule, expressed in grams per mole. The molecular formula represents the actual number of each type of atom in a molecule. By using the data from combustion analysis and the Ideal Gas Law, one can calculate the molecular weight and derive the molecular formula of methyl tert-butyl ether, providing insight into its chemical structure and properties.

Recommended video:

Guided course

02:08

Determining Molecular Formulas

Related Practice

Textbook Question

Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to 20,000 mi/h). For example, explosion of nitroglycerin (C₃H₅N₃O₉) releases four gases, A, B, C, and D:

n C₃H₅N₃O₉(l) a A(g) + b B(g) + c C(g) + d D(g)

Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure.

(d) When gases C and D were passed through a hot tube of powdered copper, gas C reacted to form CuO. The remaining gas, D, was collected in a third 500.0-mL flask and found to have a mass of 0.168 g and a pressure of 223 mm Hg at 25 °C. How many moles each of C and D were present, and what are their likely identities?

602

views

Textbook Question

n C₃H₅N₃O₉(l) a A(g) + b B(g) + c C(g) + d D(g)

Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure.

(e) Write a balanced equation for the explosion of nitroglycerin.

916

views

Textbook Question

Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO₂ and 0.1838 g of H₂O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g. (a) What is the empirical formula of methyl tert-butyl ether?

321

views

Textbook Question

Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO₂ and 0.1838 g of H₂O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g. (c) Write a balanced equation for the combustion reaction.

304

views

Textbook Question

During a certain time period, 4.0 million tons of SO2 were released into the atmosphere and subsequently oxidized to SO3. As explained in the Inquiry, the acid rain produced when the SO3 dissolves in water can damage marble statues: CaCO31s2 + H2SO41aq2S CaSO41aq2 + CO21g2 + H2O1l2 (b) How many liters of CO2 gas at 20 °C and 735 mm Hg is produced as a byproduct?.

347

views