Question

An expensive vacuum system can achieve a pressure as low as 1.00×10−⁷ N/m² at 20.0°C. How many molecules are there in a cubic centimeter at this pressure and temperature?

a) 2.7 × 10¹⁹
b) 5.4 × 10¹⁹
c) 8.1 × 10¹⁹
d) 1.1 × 10²⁰

Answer 1

To calculate the number of molecules in a cubic centimeter at a given pressure and temperature, we can use the ideal gas law. Using the given values, the number of molecules is found to be 2.694 × 10¹⁹ molecules.

Step-by-step explanation:

To calculate the number of molecules in a cubic centimeter at a given pressure and temperature, we can use the ideal gas law. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Rearranging this equation, we have n = PV / RT.

First, we need to convert the pressure to Pascal (1 N/m² = 1 Pascal). So, our pressure of 1.00 × 10⁻⁷ N/m² is equal to 1.00 × 10⁻⁷ Pascal. Next, we convert the volume to cubic meters since the ideal gas constant R has units of J/(mol·K). A cubic centimeter is equal to 1 × 10⁻⁶ cubic meters.

Using the given values, we can substitute them into the equation n = PV / RT. n = (1.00 × 10⁻⁷ Pascal) × (1 × 10⁻⁶ m³) / [(8.314 J/(mol·K)) × (20.0°C + 273.15)] = 2.694 × 10¹⁹ molecules.