Gas Law Calculation: Volume at Different Conditions

What is the new volume of a sample of N₂ gas at a pressure of 3.50 atm and a temperature of 226°C?

Given data:

- Initial volume: 19.0 L

- Initial pressure: 1.50 atm

- Initial temperature: 23°C

Answer:

The new volume of the N₂ gas at a pressure of 3.50 atm and a temperature of 226°C will be calculated using the combined gas law.

The question requires us to determine the new volume of the N₂ gas when the pressure and temperature are changed. The combined gas law, which combines Boyle's Law, Charles's Law, and Gay-Lussac's Law, is used to solve this type of problem.

We are given the initial volume, pressure, and temperature of the gas, along with the new pressure and temperature values. By applying the combined gas law formula P1V1/T1 = P2V2/T2, we can solve for the final volume of the gas.

Firstly, we need to convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. Therefore, T1 = 23°C + 273.15 = 296.15 K and T2 = 226°C + 273.15 = 499.15 K.

Next, we can plug in the provided values into the formula:

V2 = (P1 * V1 * T2) / (P2 * T1)

By substituting the known values into the equation and performing the calculations, we can determine the new volume of the N₂ gas at the specified conditions.