Question

A sample of Freon- \(12\left(\mathrm{CF}_{2} \mathrm{Cl}_{2}\right.\) ) occupies \(25.5 \mathrm{~L}\) at \(298 \mathrm{~K}\) and \(153.3 \mathrm{kPa}\). Find its volume at \(\mathrm{STP}\).

Short answer

35.37 L

Step-by-step solution

Identify given values

Given: Initial volume (\(V_1\right)\) = 25.5 L, Initial temperature (\(T_1\right)\) = 298 K, Initial pressure (\(P_1\right)\) = 153.3 kPa.

Note STP conditions

Standard Temperature and Pressure (STP) conditions are: Temperature (\(T_2\right)\) = 273 K, Pressure (\(P_2\right)\) = 100 kPa.

Use Combined Gas Law

The Combined Gas Law formula is \ \( \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \). Rearrange this formula to solve for the final volume \ (\(V_2\right)\): \ \[ V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1} \]

Substitute the values

Substitute the known values into the rearranged formula: \ \[ V_2 = \frac{153.3 \text{kPa} \times 25.5 \text{L} \times 273 \text{K}}{100 \text{kPa} \times 298 \text{K}} \]

Calculate

Calculate the final volume (\(V_2\right)\): \ \[ V_2 = \frac{153.3 \times 25.5 \times 273}{100 \times 298} \] \ \[ V_2 \approx \35.37 \text{ L} \]

Key concepts

Gas Laws

Gas laws are essential principles that describe the behavior of gases. They help us understand how changes in pressure, volume, and temperature affect a gas. The combined gas law merges Boyle’s, Charles’s, and Gay-Lussac’s laws into one equation: \[ \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \] This equation allows us to solve for any one of the variables if the others are known. By using the combined gas law, we can predict how a gas will behave under different conditions. Remember that temperatures should always be in Kelvin for these calculations.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, or STP, is a reference point used in gas law calculations to provide consistency. At STP, the temperature is set to 273 K (0°C) and the pressure is 100 kPa (approximately 1 atmosphere). Using STP allows scientists and engineers to compare data without variations caused by differing conditions. When a problem involves changing conditions to or from STP, it is essential to use these standard values.
In our example, we are required to find the volume of Freon-12 at STP.

Freon-12

Freon-12, or Dichlorodifluoromethane, is a type of chlorofluorocarbon (CFC) represented by the chemical formula \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\). It has been commonly used as a refrigerant and aerosol spray propellant. Due to its environmental impact, notably its role in ozone layer depletion, its usage has been heavily regulated and phased out under international agreements. In gas law problems involving Freon-12 or any other gas, the chemical identity often influences practical uses but doesn’t typically change the formula application unless the gas behaves non-ideally.

Volume Calculation

Volume calculation in gas law problems requires careful substitution into the combined gas law. To find the new volume (\( V_2 \)) of a gas when conditions change, we rearrange the formula: \[ V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1} \].
For our specific exercise involving Freon-12:
Using the given data: \( V_1 = 25.5 \text{ L} \), \( P_1 = 153.3 \text{ kPa} \), \( T_1 = 298 \text{ K} \), and STP conditions \( P_2 = 100 \text{ kPa} \), \( T_2 = 273 \text{ K} \), we substitute these values into the formula to solve for \( V_2 \): \[ V_2 = \frac{153.3 \times 25.5 \times 273}{100 \times 298} \].
After performing the calculation, we find \( V_2 \approx 35.37 \text{ L} \). This result shows the volume of Freon-12 at STP.

Pressure

Pressure is the force exerted by gas particles hitting the walls of their container. It is measured in various units, including kPa (kilopascal), atm (atmospheres), and mmHg (millimeters of mercury).
In gas law problems, understanding whether pressure increases or decreases is crucial as it inversely affects volume (Boyle’s Law) if temperature remains constant. In our exercise, the initial pressure is 153.3 kPa, but we need the final volume at STP (100 kPa). This reduction in pressure, in conjunction with the temperature change, results in a new volume that is calculable through the combined gas law.
Remember, when handling gas law equations, always ensure that the units for pressure are consistent to avoid errors in calculation.