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.

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Convert the pressure from torr to atmospheres (atm) since the ideal gas law uses pressure in atm. Recall that 1 atm = 760 torr.

Use the ideal gas law, which is PV = nRT, where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles of gas, R is the ideal gas constant (0.0821 L atm / K mol), and T is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

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

Convert the number of moles of gas to number of molecules by using Avogadro's number (6.022 x 10^23 molecules/mol). Multiply the number of moles by Avogadro's number to find the number of molecules.

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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 number of moles of gas present under specific conditions, which is essential for determining the number of molecules.

Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. However, conditions such as temperature and pressure can affect this volume. In this question, we need to adjust the calculations for the given temperature (37°C) and pressure (735 torr) to find the actual volume occupied by one mole of air, which will help in determining the number of molecules in the specified volume.

Avogadro's Number

Avogadro's Number, approximately 6.022 x 10²³, is the number of molecules in one mole of a substance. This constant is crucial for converting between moles and molecules. Once we calculate the number of moles of air in the 2.25 L volume using the Ideal Gas Law, we can multiply by Avogadro's Number to find the total number of molecules present in that volume.

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Avogadro's Law

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