Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 61

A 2.00 L container is filled with \(\operatorname{Ar}(g)\) at 752 mm Hg and \(35^{\circ} \mathrm{C} .\) A \(0.728 \mathrm{g}\) sample of \(\mathrm{C}_{6} \mathrm{H}_{6}\) vapor is then added. (a) What is the total pressure in the container? (b) What is the partial pressure of \(\mathrm{Ar}\) and of \(\mathrm{C}_{6} \mathrm{H}_{6} ?\)

Short Answer

Expert verified
(a) The total pressure in the vessel is the sum of the partial pressures of $\mathrm{Ar}(g)$ and $\mathrm{C}_{6} \mathrm{H}_{6}$. (b) The partial pressure of each gas in the mixture can be determined using their respective mole fractions along with the total pressure.

Step by step solution

01

Convert the given values to appropriate units

The temperature will be converted from Celsius to Kelvin by using the formula \[T(K) = T(°C) + 273.15\]. The volume is already in litres and the initial pressure of Ar(g) is in mm Hg. Convert this to atmospheres by using \(1 \, \text{atm} = 760 \, \text{mm Hg}\).
02

Applying the ideal gas law to Ar(g)

The ideal gas law, \(PV = nRT\), is used to calculate the number of moles of Ar(g), since the volume, pressure and temperature are known. Here, R is the ideal gas constant and its value is \(0.0821 \, \text{L atm/mol K}\).
03

Calculate the number of moles of C6H6

The number of moles of \(C_6H_6\) can be calculated by using the molar mass of \(C_6H_6\), which is approximately 78.11 g/mol. Here, \(n = \text{mass} / \text{molar mass}\).
04

Calculate total pressure using Dalton's Law

Dalton's Law states that the total pressure exerted by a mixture of gases is the sum of the partial pressures of each individual gas. The total pressure is given by the equation \(P_{\text{total}} = n_{\text{total}}RT / V\), where \(n_{\text{total}}\) is the sum of the number of moles of Ar(g) and \(C_6H_6\).
05

Calculate the partial pressure for Ar(g) and C6H6

The partial pressure of each gas can be found using the formula \(P_{i} = X_{i}P_{\text{total}}\), where \(X_{i}\) is the mole fraction of the gas in the mixture and is given by the number of moles of the gas divided by the total number of moles in the mixture.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A gaseous hydrocarbon that is \(82.7 \%\) C and \(17.3 \%\) H by mass has a density of \(2.35 \mathrm{g} / \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and 752 Torr. What is the molecular formula of this hydrocarbon?

At what temperature is the molar volume of an ideal gas equal to \(22.4 \mathrm{L},\) if the pressure of the gas is \(2.5 \mathrm{atm} ?\)

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is sometimes used as a chlorinating agent for water treatment. It can be prepared from the reaction below: \(\mathrm{Cl}_{2}(\mathrm{g})+4 \mathrm{NaClO}(\mathrm{aq}) \longrightarrow 4 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{ClO}_{2}(\mathrm{g})\) In an experiment, \(1.0 \mathrm{L} \mathrm{Cl}_{2}(\mathrm{g}),\) measured at \(10.0^{\circ} \mathrm{C}\) and 4.66 atm, is dissolved in 0.750 L of 2.00 M \(\mathrm{NaClO}(\mathrm{aq}) .\) If \(25.9 \mathrm{g}\) of pure \(\mathrm{ClO}_{2}\) is obtained, then what is the percent vield for this experiment?

At times, a pressure is stated in units of mass per unit area rather than force per unit area. Express \(P=1 \mathrm{atm}\) in the unit \(\mathrm{kg} / \mathrm{cm}^{2}\) [Hint: How is a mass in kilograms related to a force?]

Explain why the height of the mercury column in a barometer is independent of the diameter of the barometer tube.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free