Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.10 - Gases

Problem 68b

Chapter 10, Problem 68b

A sample of 5.00 mL of diethyl ether (C2H5OC2H5,density=0.7134 g/mL) is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are 𝑃N2=0.751atm and 𝑃O2=0.208atm. The temperature is held at 35.0°C, and the diethyl ether totally evaporates. b. Calculate the total pressure in the container.

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Calculate the mass of diethyl ether using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).

Convert the mass of diethyl ether to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).

Use the ideal gas law to find the partial pressure of diethyl ether: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Add the partial pressures of N2, O2, and diethyl ether to find the total pressure in the container: \( P_{\text{total}} = P_{\text{N2}} + P_{\text{O2}} + P_{\text{ether}} \).

Ensure all pressures are in the same units (e.g., atm) before adding them to find the total pressure.

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Key Concepts

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

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 essential for understanding how gases behave under varying conditions and is crucial for calculating the total pressure in a container after the diethyl ether evaporates.

Partial Pressure

Partial pressure is the pressure exerted by an individual gas in a mixture of gases. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of each component. This concept is vital for determining the total pressure in the vessel after the diethyl ether has evaporated and contributed to the gas mixture.

Density and Mass Calculation

Density is defined as mass per unit volume and is used to convert between the volume of a substance and its mass. In this problem, the density of diethyl ether allows us to calculate the mass of the ether introduced into the vessel, which is necessary for determining the number of moles of gas produced upon evaporation.

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