Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 100

To minimize the rate of evaporation of the tungsten filament, \(1.4 \times 10^{-5}\) mol of argon is placed in a \(600-\mathrm{cm}^{3}\) light-bulb. What is the pressure of argon in the lightbulb at \(23^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The pressure of argon inside the lightbulb at \(23^\circ C\) is approximately \(5.38 \times 10^{-5}\) atm.

Step by step solution

01

Convert the temperature to Kelvin

To calculate the pressure of argon, we need the temperature in Kelvin. To convert Celsius to Kelvin, add 273.15 to the given temperature. \(T(K) = 23^\circ C + 273.15\) \(T(K) = 296.15 K\)
02

Convert volume to liters

The volume of the lightbulb is given in cubic centimeters (cm³), but we need the volume in liters (L) to use the Ideal Gas Law. To convert cm³ to L, divide the volume by 1000. \(V(L) = 600 \text{ cm}^3 \times \frac{1 \text{ L}}{1000 \text{ cm}^3}\) \(V(L) = 0.600 \text{ L}\)
03

Find the universal gas constant value

The universal gas constant (R) has various different units. We will use the unit that has L atm / mol K to be consistent with our given values. \(R = 0.0821 \frac{\text{L atm}}{\text{mol K}}\)
04

Apply the Ideal Gas Law formula

Now, we have all the information we need to apply the Ideal Gas Law formula and solve for pressure (P). \(PV = nRT\) Rearrange the formula to solve for P: \(P = \frac{nRT}{V}\) Plug in the values: \(P = \frac{(1.4 \times 10^{-5} \text{ mol})(0.0821 \frac{\text{L atm}}{\text{mol K}})(296.15 \text{ K})}{0.600 \text{ L}}\)
05

Calculate the pressure

Now, we simply perform the calculation in the formula. \(P = \frac{(1.4 \times 10^{-5})(0.0821)(296.15)}{0.600}\) \(P = 5.38 \times 10^{-5} \text{ atm}\) The pressure of argon inside the lightbulb at \(23^\circ C\) is approximately \(5.38 \times 10^{-5}\) atm.

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

An ideal gas at a pressure of 1.50 atm is contained in a bulb of unknown volume. A stopcock is used to connect this bulb with a previously evacuated bulb that has a volume of 0.800 \(\mathrm{L}\) as shown here. When the stopcock is opened, the gas expands into the empty bulb. If the temperature is held constant during this process and the final pressure is 695 torr, what is the volume of the bulb that was originally filled with gas?

You have a gas at \(25^{\circ} \mathrm{C}\) confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? \((\mathbf{a})\) Lifting up on the piston to double the volume while keeping the temperature constant; \((\mathbf{b})\) Heating the gas so that its temperature rises from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) , while keeping the volume constant; \((\mathbf{c})\) Pushing down on the piston to halve the volume while keeping the temperature constant.

A mixture containing 0.765 mol \(\mathrm{He}(g), 0.330 \mathrm{mol} \mathrm{Ne}(g),\) and 0.110 \(\mathrm{mol} \mathrm{Ar}(g)\) is confined in a \(10.00-\mathrm{L}\) vessel at \(25^{\circ} \mathrm{C}\) . (a) Calculate the partial pressure of each of the gases in the mixture. (b) Calculate the total pressure of the mixture.

Consider a mixture of two gases, \(A\) and \(B,\) confined in a closed vessel. A quantity of a third gas, \(C,\) is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A, (b) the total pressure in the vessel, (c) the mole fraction of gas B?

Suppose you have two 1 -L flasks, one containing \(\mathrm{N}_{2}\) at STP, the other containing \(\mathrm{CH}_{4}\) at STP. How do these systems compare with respect to (a) number of molecules, (b) density, (c) average kinetic energy of the molecules, (d) rate of effusion through a pinhole leak?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Reactions

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

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