Skip to main content
Ch.10 - Gases
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.10 - GasesProblem 64
Chapter 10, Problem 64

A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 °C.

Verified step by step guidance
1
Step 1: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary because gas law calculations require temperature in Kelvin.
Step 2: Calculate the number of moles of each gas using the formula \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass of the gas, and \( M \) is the molar mass of the gas. Use the molar mass of O2 (32.00 g/mol) and He (4.00 g/mol).
Step 3: Use the ideal gas law \( PV = nRT \) to calculate the partial pressure of each gas. Rearrange the formula to \( P = \frac{nRT}{V} \), where \( P \) is the pressure, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), \( T \) is the temperature in Kelvin, and \( V \) is the volume in liters.
Step 4: Calculate the partial pressure of O2 by substituting the number of moles of O2, the ideal gas constant, the temperature in Kelvin, and the volume of the cylinder into the rearranged ideal gas law equation.
Step 5: Calculate the partial pressure of He using the same method as in Step 4, substituting the number of moles of He. Then, add the partial pressures of O2 and He to find the total pressure in the gas cylinder.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the behavior of gases under various conditions, allowing us to determine the pressure exerted by a gas in a given volume at a specific temperature.
Recommended video:
Guided course
01:15
Ideal Gas Law Formula

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas, which is crucial for solving the problem at hand.
Recommended video:
Guided course
00:48
Partial Pressure Calculation

Molar Mass and Moles Calculation

To calculate the partial pressures, it is necessary to convert the mass of each gas into moles using their respective molar masses. This conversion is vital for applying the Ideal Gas Law, as the number of moles (n) directly influences the pressure calculation for each gas in the mixture.
Recommended video:
Guided course
03:12
Molar Mass Calculation Example
Related Practice
Textbook Question

A sample of 5.00 mL of diethyl ether (C2H5OC2H5,density=0.7134 g/mL) is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are 𝑃N2=0.751atm and 𝑃O2=0.208atm. The temperature is held at 35.0°C, and the diethyl ether totally evaporates. b. Calculate the total pressure in the container.

Textbook Question

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, how does the volume occupied by the N2 gas change?

683
views
Textbook Question

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?

835
views
Textbook Question

The atmospheric concentration of CO2 gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every 106 L of the atmosphere are CO2). What is the mole fraction of CO2 in the atmosphere?.

1953
views
Textbook Question

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 g is placed in a 10.0-L vessel that already contains air at 705 torr and 24°C. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO2 gas, and the total pressure in the container, at 24°C?