Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 12

A sealed syringe has \(25.0 \mathrm{~mL}\) of air at \(23^{\circ} \mathrm{C}\) and \(745 \mathrm{~mm} \mathrm{Hg}\) pressure. The syringe is transferred to a water bath maintained at \(82^{\circ} \mathrm{C}\). The volume of the gas in the syringe increased by \(8.0 \%\). What is the pressure in the syringe? Did the pressure increase?

Short Answer

Expert verified
The final pressure in the syringe is approximately 776.81 mm Hg. This is an increase in pressure compared to the initial pressure of 745 mm Hg.

Step by step solution

01

Write down the given information

We have these initial values: - Initial volume: \(V_1 = 25.0 \mathrm{~mL}\) - Initial temperature: \(T_1 = 23^{\circ} \mathrm{C}\) - Initial pressure: \(P_1 = 745 \mathrm{~mm} \mathrm{Hg}\) And these final values: - Final volume: \(V_2 = 1.08V_1\) (increased by \(8.0 \%\)) - Final temperature: \(T_2 = 82^{\circ} \mathrm{C}\) - Final pressure: \(P_2\) (need to find out)
02

Convert Celsius to Kelvin

We need to convert the temperatures in Celsius to Kelvin (\(K\)) for the combined gas law calculation. - \(T_1 = 23^{\circ} \mathrm{C} + 273.15 \mathrm{K} = 296.15 \mathrm{K}\) - \(T_2 = 82^{\circ} \mathrm{C} + 273.15 \mathrm{K} = 355.15 \mathrm{K}\)
03

Apply the combined gas law

The combined gas law relates initial and final pressures, volumes, and temperatures of a gas as follows: $$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$ We will solve for \(P_2\): $$P_2 = \frac{P_1V_1T_2}{T_1V_2}$$
04

Substitute the values and calculate \(P_2\)

Now, replace the variables with their corresponding values: $$P_2 = \frac{745 \mathrm{~mm} \mathrm{Hg} \times 25.0 \mathrm{~mL} \times 355.15 \mathrm{K}}{296.15 \mathrm{K} \times 1.08 \times 25.0 \mathrm{~mL}}$$ Simplify and calculate \(P_2\): $$P_2 \approx 776.81 \mathrm{~mm} \mathrm{Hg}$$
05

Compare \(P_1\) and \(P_2\) to determine whether the pressure increased

Comparing the initial pressure \(P_1 = 745 \mathrm{~mm} \mathrm{Hg}\) and the final pressure \(P_2 \approx 776.81 \mathrm{~mm} \mathrm{Hg}\), we can conclude that the pressure increased since \(P_2 > P_1\).

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

Glycine is an amino acid made up of carbon, hydrogen, oxygen, and nitrogen atoms. Combustion of a \(0.2036\) -g sample gives \(132.9 \mathrm{~mL}\) of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) and \(0.122 \mathrm{~g}\) of water. What are the percentages of carbon and hydrogen in glycine? Another sample of glycine weighing \(0.2500 \mathrm{~g}\) is treated in such a way that all the nitrogen atoms are converted to \(\mathrm{N}_{2}(g)\). This gas has a volume of \(40.8 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\). What is the percentage of nitrogen in glycine? What is the percentage of oxygen? What is the empirical formula of glycine?

In Calculate the densities (in grams per liter) of the following gases at \(97^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) (a) hydrogen chloride (b) sulfur dioxide (c) butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\)

A certain laser uses a gas mixture consisting of \(9.00 \mathrm{~g} \mathrm{HCl}, 2.00 \mathrm{~g} \mathrm{H}_{2}\) and \(165.0 \mathrm{~g}\) of Ne. What pressure is exerted by the mixture in a \(75.0\) -L tank at \(22^{\circ} \mathrm{C}\) ? Which gas has the smallest partial pressure?

What is the ratio of the rate of effusion of the most abundant gas, nitrogen, to the lightest gas, hydrogen?

An intermediate reaction used in the production of nitrogencontaining fertilizers is that between ammonia and oxygen: $$ 4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ A \(150.0\) - \(\mathrm{L}\) reaction chamber is charged with reactants to the following partial pressures at \(500^{\circ} \mathrm{C}: P_{\mathrm{NH}_{3}}=1.3 \mathrm{~atm}, P_{\mathrm{O}_{2}}=1.5 \mathrm{~atm} .\) What is the limiting reactant?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

The Earths Atmosphere

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