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?

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.

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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?

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Complete the following table for an ideal gas:

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