Question

In the air we breathe at 76.0 ∘F and 0.930 atm pressure, how many molecules does a typical cubic centimeter contain, assuming that the air is all N₂. express your answer as number of molecules.

Answer 1

To find the number of molecules in a cubic centimeter of N₂ at 76.0 °F and 0.930 atm, convert the given conditions to Kelvin and liters, use the Ideal Gas Law to solve for moles, and then multiply by Avogadro's number.

Step-by-step explanation:

To calculate the number of molecules in a cubic centimeter of N₂ at 76.0 °F and 0.930 atm, we can use the Ideal Gas Law: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

First, convert the temperature to Kelvin and the volume to liters:

Temperature: 76.0 °F = 24.44 °C = 297.59 K

Volume: 1 cm³ = 1×⁻⁳ L

Next, rearrange the Ideal Gas Law to solve for n, the number of moles: n = PV/RT. We then convert moles to molecules by multiplying by Avogadro's number (6.022×ⁱ²³ molecules/mol).

Plugging the known values into the equation:

n = (0.930 atm × 1×⁻⁳ L) / (0.0821 L·atm/K·mol × 297.59 K)

The result gives the number of moles in 1 cm³ at the given conditions.

Multiply that by Avogadro's number to find the number of molecules.

The exact calculation needs to be carried out to find the final number of molecules, which is not provided here as this is an instructional example.