(a) 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 97.99 kPa.

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).
2. 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 L·kPa/mol·K), and \( T \) is the temperature in Kelvin.
3. Rearrange the Ideal Gas Law equation to solve for \( n \): \( n = \frac{PV}{RT} \).
4. Substitute the given values for \( P \), \( V \), and \( T \) into the equation to calculate \( n \).
5. Calculate the number of molecules by multiplying the number of moles \( n \) by Avogadro's number \( 6.022 \times 10^{23} \) molecules/mol.

Key Concepts

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 molecules in a given volume of gas under specific conditions.

Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies approximately 22.4 liters. However, at different temperatures and pressures, the volume occupied by one mole of gas changes. Understanding how to adjust for these conditions is crucial for calculating the number of molecules in a specific volume of gas, as seen in the context of the question.

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 essential for converting between moles and molecules, allowing chemists to quantify the number of particles in a given sample. In the context of the question, once the number of moles is calculated using the Ideal Gas Law, Avogadro's Number can be used to find the total number of molecules in the air sample.