Question

Calculate the number of molecules in a deep breath of air whose volume is \(2.25 \mathrm{~L}\) at body temperature, \(37^{\circ} \mathrm{C}\), and a pressure of 735 torr.

Short answer

There are approximately \(4.93 × 10^{22}\) molecules in a deep breath of air whose volume is 2.25 L at body temperature and pressure of 735 torr.

Step-by-step solution

Convert pressure unit from torr to atm and volume unit to dm³.

To use the ideal gas law equation, we should convert the pressure in torr into atm and the volume in liters to dm³. 1 atm = 760 torr 1 L = 1 dm³ So, Pressure (P) = 735 torr × (1 atm / 760 torr) = 0.9671 atm Volume (V) = 2.25 L = 2.25 dm³

Convert temperature to Kelvin.

In order to use the ideal gas law equation, we need to convert the temperature from Celsius to Kelvin. Temperature (T) = 37°C + 273.15 = 310.15 K

Use the ideal gas equation to find the number of moles.

Now we can use the ideal gas law equation to find the number of moles (n). The ideal gas constant (R) is given in the units of L·atm/mol·K or dm³·atm/mol·K, which is 0.0821 dm³·atm/mol·K. \(PV = nRT\) n = PV / RT n = (0.9671 atm) × (2.25 dm³) / [(0.0821 dm³·atm/mol·K) × (310.15 K)] n = 0.0819 moles

Calculate the number of molecules using Avogadro's number.

Now that we have the number of moles, we can convert it into the number of molecules using Avogadro's number, which is approximately 6.022 × 10²³ molecules/mol. Number of molecules = n × Avogadro's number Number of molecules = 0.0819 moles × (6.022 × 10²³ molecules/mol) Number of molecules = 4.93 × 10²² molecules There are approximately \(4.93 × 10^{22}\) molecules in a deep breath of air whose volume is 2.25 L at body temperature and pressure of 735 torr.