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.

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Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For this problem, convert 0.0°C to Kelvin.

Substitute the values into the ideal gas law equation. Use P = 1.00 atm, V = 5000 L (converted from 5.0×10^3 L), R = 0.0821 L·atm/mol·K (the value of R when pressure is in atm and volume is in liters), and T = the Kelvin temperature from step 2.

Solve the ideal gas law equation for n, the number of moles of gas, by rearranging the equation to n = PV / RT.

Calculate the mass of the air in the lungs by multiplying the number of moles (n) by the average molar mass of air (28.98 g/mol).

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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 volumes and masses.

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 calculations involving the Ideal Gas Law. In this problem, the average molar mass of air (28.98 g/mol) is used to determine the mass of air contained in the blue whale's lungs.

Gas Density

Gas density is defined as the mass of a 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, the density of air at the given conditions can be derived from the Ideal Gas Law, allowing for the determination of the total mass of air in the whale's lungs.

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