(b) 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 101.33 kPa, assuming the air behaves ideally.

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Identify the given values: lung capacity (volume) = 5.0 \(\times\) 10^3 \(\text{ L}\), temperature = 0.0 \, ^\(\circ\)\(\text{C}\), pressure = 101.33 \, \(\text{kPa}\), and molar mass of air = 28.98 \, \(\text{g/mol}\).

Convert the temperature from Celsius to Kelvin using the formula: \( T(\text{K}) = T(\text{°C}) + 273.15 \).

Use the ideal gas law equation \( PV = nRT \) to solve for the number of moles \( n \). Here, \( P \) is the pressure in kPa, \( V \) is the volume in liters, \( R \) is the ideal gas constant (8.314 \(\text{ L kPa K}\)^{-1} \(\text{ mol}\)^{-1}), and \( T \) is the temperature in Kelvin.

Rearrange the ideal gas law to solve for \( n \): \( n = \frac{PV}{RT} \). Substitute the known values into the equation to find \( n \).

Calculate the mass of air using the formula: mass = \( n \times \text{molar mass} \). Substitute the value of \( n \) and the molar mass of air to find the mass.

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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 behavior of gases under various conditions, making it essential for solving problems involving gas calculations.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a crucial concept for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. In this problem, the average molar mass of air (28.98 g/mol) is used to determine the mass of air contained in the whale's lungs after calculating the number of moles using the Ideal Gas Law.

Gas Density

Gas density is defined as the mass of gas per unit volume, often expressed in grams per liter (g/L). Understanding gas density is important for calculating the mass of a gas when its volume and molar mass are known. In this scenario, once the number of moles of air is determined using the Ideal Gas Law, the mass can be calculated by multiplying the number of moles by the molar mass, providing insight into the total mass of air in the whale's lungs.

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