Question

A. How many molecules are present in a sample of an ideal gas that occupies a volume of 1.60 cm3, is at a temperature of 20°C, and is at atmospheric pressure?

B. How many molecules of the gas are present if the volume and temperature are the same as in part (a), but the pressure is now 2.30 ✕ 10−11 Pa (an extremely good vacuum)?

Answer 1

Using the ideal gas law (PV = nRT), we can calculate the number of moles of an ideal gas under specified conditions and then convert it to the number of molecules using Avogadro's number (6.022 × 10²³ molecules/mol). Part A involves standard atmospheric pressure, while Part B involves an extremely low vacuum pressure.

Step-by-step explanation:

To find out how many molecules are present in a sample of an ideal gas at a given volume, temperature, and pressure, we can use the ideal gas law equation, which is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in kelvin.

For part A: The conditions are 1.60 cm³ of volume, 20°C (which converts to 293 K), at atmospheric pressure (1.013 × 10⁵ Pa). Since we expect to find a very small number of moles, we can use Avogadro's number (6.022 × 10²³ molecules/mol) to convert moles to molecules once we solve for n.

For part B: The volume (1.60 cm³) and temperature (20°C or 293 K) are the same, but the pressure is now 2.30 × 10⁻¹¹ Pa. We apply the ideal gas law similarly, but we'll get a different number of moles due to the lower pressure, and can again use Avogadro's number to find the number of molecules.