Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (b) What volume will the Cl₂ occupy at STP?

Verified step by step guidance

1. Identify the initial conditions: Volume (V1) = 8.70 L, Pressure (P1) = 119.3 kPa, Temperature (T1) = 24 °C.
2. Convert the initial temperature from Celsius to Kelvin using the formula: T(K) = T(°C) + 273.15.
3. Identify the conditions at STP: Pressure (P2) = 101.3 kPa, Temperature (T2) = 273.15 K.
4. Use the combined gas law to relate the initial and final states: \( \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \).
5. Rearrange the equation to solve for the final volume \( V_2 \): \( V_2 = \frac{P_1 \times V_1 \times T_2}{T_1 \times P_2} \).

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and allows for the calculation of one variable when the others are known.

Standard Temperature and Pressure (STP)

STP is defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm (101.3 kPa). At STP, one mole of an ideal gas occupies 22.4 L. Understanding STP is crucial for converting gas volumes from one set of conditions to another.

Gas Volume Conversion

Gas volume conversion involves using the Ideal Gas Law and the conditions of STP to determine how the volume of a gas changes with variations in temperature and pressure. This concept is key for solving problems that require finding the volume of a gas under different environmental conditions.