The Goodyear blimps, which frequently fly over sporting events, hold approximately 4955 m3 of helium. If the gas is at 23 °C and 101.33 kPa, what mass of helium is in a blimp?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780137542970

Verified step by step guidance

Step 1: Use the Ideal Gas Law equation, PV = nRT, to find the number of moles (n) of helium. Here, P is the pressure (101.33 kPa), V is the volume (4955 m^3), R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin (23 °C + 273.15).

Step 2: Convert the pressure from kPa to Pa by multiplying by 1000, since the ideal gas constant R is in J/(mol·K) and 1 J = 1 Pa·m^3.

Step 3: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Step 4: Rearrange the Ideal Gas Law equation to solve for n (number of moles): n = PV / RT.

Step 5: Calculate the mass of helium by multiplying the number of moles (n) by the molar mass of helium (4.00 g/mol).

Key Concepts

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

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the properties of gases under various conditions.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For helium, the molar mass is approximately 4.00 g/mol. Understanding molar mass is essential for converting between the mass of a gas and the number of moles, which is necessary for applying the Ideal Gas Law.

Gas Density

Gas density is defined as the mass of a gas per unit volume, usually expressed in grams per liter (g/L). It can be calculated using the formula density = mass/volume. Knowing the density of a gas allows for the determination of its mass when the volume is known, which is crucial for solving problems involving gas quantities.

Recommended video:

Guided course

01:21

Gas Density Example

Related Practice

Textbook Question

The adult blue whale has a lung capacity of 5.0×103 L. Calculate the mass of air (assume an average molar mass of 28.98 g/mol) contained in an adult blue whale’s lungs at 0.0°C and 1.00 atm, assuming the air behaves ideally.

Textbook Question

Complete the following table for an ideal gas:

Textbook Question

Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x atm. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

Textbook Question

Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, 37°C, and a pressure of 735 torr.