Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 1233

\(2 \mathrm{~g}\) of \(\mathrm{O}_{2}\) gas is taken at \(27^{\circ} \mathrm{C}\) and pressure \(76 \mathrm{~mm} \mathrm{Hg}\). Find out volume of gas (ln liter) (A) \(3.08\) (B) \(44.2\) (C) \(2.05\) (D) \(2.44\)

Short Answer

Expert verified
The volume of the gas is approximately 2.05 liters. The correct answer is (C).

Step by step solution

01

Convert the given mass of O₂ to moles

We are given the mass of O₂ (2 grams). To find the number of moles, we need to divide the mass by the molar mass of O₂. The molar mass of O₂ is 16 g/mol (for each oxygen atom) multiplied by 2 (since there are two oxygen atoms in a molecule of O₂), which is 32 g/mol: Number of moles (n) = (mass of O₂) / (molar mass of O₂) n = 2 g / 32 g/mol = 1/16 mol
02

Convert temperature to Kelvin

The given temperature (T) is 27°C. We need to convert this to Kelvin, because the ideal gas law requires the temperature to be in Kelvin. To do this, simply add 273.15: T = 27°C + 273.15 = 300.15 K
03

Convert pressure to atmospheres

We are given the pressure of the gas in mm Hg. To use the ideal gas law, we need to convert the pressure to atmospheres. Since there are 760 mm Hg in 1 atmosphere, we have: Pressure (P) = 76 mm Hg * (1 atm / 760 mm Hg) = 0.1 atm
04

Use the ideal gas law to find the volume

We now have all the necessary information to use the ideal gas law (PV=nRT). The only unknown is the volume (V). We can rearrange the equation to solve for V: V = nRT / P Now plug in the necessary values. The universal gas constant (R) is always 0.0821 L⋅atm/(mol⋅K): V = (1/16 mol)(0.0821 L⋅atm/(mol⋅K))(300.15 K) / (0.1 atm)
05

Calculate the volume of the gas

Now perform the computation: V = (1/16)(0.0821)(300.15) / (0.1) V ≈ 2.046 The volume of the gas is approximately 2.05 liters. The correct answer is (C).

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 gas at \(27{ }^{\circ} \mathrm{C}\) temperature and 30 atmospheric pressure $1 \mathrm{~s}$ allowed to expand to the atmospheric pressure if the volume becomes two times its initial volume, then the final temperature becomes (A) \(273^{\circ} \mathrm{C}\) (B) \(-173^{\circ} \mathrm{C}\) (C) \(173^{\circ} \mathrm{C}\) (D) \(100^{\circ} \mathrm{C}\)

A diatomic gas molecule has translational, rotational and vibrational degrees of freedom. The $\left(\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{V}}\right)$ is (A) \(1.29\) (B) \(1.33\) C) \(1.4\) (D) \(1.67\)

At what temperature pressure remaining constant will the \(\mathrm{rms}\) speed of a gas molecules increase by \(10 \%\) of the \(\mathrm{rms}\) speed at NTP? (A) \(57.3 \mathrm{~K}\) (B) \(57.3^{\circ} \mathrm{C}\) (C) \(557.3 \mathrm{~K}\) (D) \(-57.3^{\circ} \mathrm{C}\)

At what temperature is the kinetic energy of a gas molecule double that of its value at \(27^{\circ} \mathrm{C}\) (A) \(54^{\circ} \mathrm{C}\) (B) \(108^{\circ} \mathrm{C}\) (C) \(327^{\circ} \mathrm{C}\) (D) \(300^{\circ} \mathrm{C}\)

Suppose ideal gas equation follows \(V P^{3}=\) constant, Initial temperature and volume of the gas are \(\mathrm{T}\) and \(\mathrm{V}\) respectively. If gas expand to \(27 \mathrm{~V}\), then temperature will become (A) \(9 \mathrm{~T}\) (B) \(27 \mathrm{~T}\) (C) (T/9) (D) \(\mathrm{T}\)
See all solutions

Recommended explanations on English Textbooks

Listening and Speaking

Read Explanation

Phonetics

Read Explanation

Language and Social Groups

Read Explanation

Linguistic Terms

Read Explanation

Rhetoric

Read Explanation

Cues and Conventions

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