Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 59

A balloon is filled with \(\mathrm{H}_{2}\) gas to a volume of \(1610.2 \mathrm{~mL}\). The pressure of the gas in the balloon is \(745.4 \mathrm{~mm} \mathrm{Hg}\), and the temperature is \(22.7^{\circ} \mathrm{C}\). What is the mass in grams of the \(\mathrm{H}_{2}\) in the balloon?

Short Answer

Expert verified
The mass of hydrogen gas in the balloon is approximately 0.1342 grams.

Step by step solution

01

Write down the Ideal Gas Law equation

The Ideal Gas Law equation is given by: PV = nRT where P represents pressure, V represents volume, n represents the number of moles, R represents the Ideal Gas Constant, and T represents the temperature in Kelvin.
02

Convert given units to appropriate units

We need to convert the given pressure, volume, and temperature to the appropriate units to use the Ideal Gas Law equation. 1. Convert pressure from mmHg to atm. (1 atm = 760 mmHg) \(P = \frac{745.4 mmHg}{760 mmHg/atm} = 0.9808 atm\) 2. Convert volume from mL to L. (1 L = 1000 mL) \(V = \frac{1610.2 mL}{1000 mL/L} = 1.6102 L\) 3. Convert temperature from Celsius to Kelvin. (T(K) = T(°C) + 273.15) \(T = 22.7°C + 273.15 = 295.85 K\)
03

Use the Ideal Gas Law to find the number of moles of hydrogen gas

We have the pressure, volume, and temperature in the appropriate units, and we know that the Ideal Gas Constant R = 0.0821 atm L/mol K. We can now find the number of moles (n) by solving the Ideal Gas Law equation: \(0.9808 atm * 1.6102 L = n * 0.0821 \frac{atm L}{mol K} * 295.85 K\) Now, solve for n: \(n = \frac{0.9808 atm * 1.6102 L}{0.0821 \frac{atm L}{mol K} * 295.85 K} = 0.0671 mol\)
04

Calculate the mass of hydrogen gas

We can now find the mass of the hydrogen gas in grams using the number of moles and the molar mass of hydrogen gas. The molar mass of hydrogen gas (H2) is 2 g/mol. Mass = n * M where M is the molar mass of hydrogen gas. \(Mass = 0.0671 mol * 2 \frac{g}{mol} = 0.1342 g\) The mass of hydrogen gas in the balloon is approximately 0.1342 grams.

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 chemistry student realizes she has forgotten the value of \(R\) and needs to determine it experimentally. She decides to measure the mass, volume, pressure, and temperature of a sample of carbon dioxide gas. She finds that \(4.505 \mathrm{~g}\) of the gas occupies \(2.50 \mathrm{~L}\) at \(23^{\circ} \mathrm{C}\) and \(0.9960 \mathrm{~atm}\). Calculate the value of \(R\) she determines from these data.

Consider a container that contains \(1.00\) mole of \(\mathrm{CO}_{2}(g)\) at \(298 \mathrm{~K}\). (a) What does the ideal gas law predict the pressure to be in atm? (b) What does the van der Waals equation predict the pressure to be? (c) What is the percent difference of the van der Waals pressure from the ideal pressure? (d) Suppose you increased the temperature to \(1000 \mathrm{~K}\). Would you expect the percent difference to increase or decrease compared to your answer in (c)? Explain.

Which variable is not needed to describe the behavior of an ideal gas: volume, number of moles, temperature, molar mass, or pressure?

(a) If the temperature of a gas is doubled while the pressure is kept constant, the volume of the gas (b) If the pressure of a gas is halved while the temperature is kept constant, the volume of the gas

"The older I get, the fewer hairs I have on my head." What kind of relationship (proportion or inverse proportion) exists between this gentleman's age and his hair? Explain your answer.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

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