Question

144\. A sample of oxygen gas has a volume of \(125 \mathrm{~L}\) at 25 ' \(\mathrm{C}\) and a pressure of 0.987 atm. Calculate the volume of this oxygen sample at STP.

Short answer

The volume of the oxygen gas sample at STP is \(114 L\).

Step-by-step solution

Convert temperature to Kelvin

To work with the gas law formula, we need to convert the given temperature from Celsius to Kelvin by adding 273.15. Also, note that STP temperature is 0°C, which is equal to 273.15 K. Initial Temperature (T1) = 25°C + 273.15 = 298.15 K STP Temperature (T2) = 273.15 K

Use the Combined Gas Law formula

The combined gas law formula is written as: (P1 * V1) / T1 = (P2 * V2) / T2 We know the initial pressure (P1), initial volume (V1), initial temperature (T1), and final pressure (P2) and temperature (T2) at STP, and our goal is to find the final volume (V2). Plugging the known values into the formula, we have: (0.987 atm * 125 L) / 298.15 K = (1 atm * V2) / 273.15 K

Solve for the final volume (V2)

To solve for V2, we will perform cross-multiplication and isolate it: V2 = (1 atm * 125 L * 273.15 K) / (0.987 atm * 298.15 K) Now, we can simplify and calculate V2: V2 ≈ (125 L * 273.15 K) / (0.987 * 298.15 K) V2 ≈ 33719.25 L·K / 294.34455 atm·K V2 ≈ 114.56 L

Round the final volume

Finally, we round the final volume to an appropriate number of significant figures. Since each of the given measurements has three significant figures, we will round the final volume to three significant figures as well: V2 = 114 L (rounded to three significant figures) Hence, the volume of the oxygen gas sample at STP is 114 L.

Key concepts

Gas Laws

Gas laws explain how gases behave under different conditions of pressure, temperature, and volume. These principles help us predict the changes in a gas when factors like pressure and temperature change. One foundational gas law is the Combined Gas Law. It integrates three fundamental laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. In essence, it defines the relationship between pressure, volume, and temperature for a fixed amount of gas.

The equation is expressed as:

• \(P_1 V_1 / T_1 = P_2 V_2 / T_2\)

where \(P\) represents pressure, \(V\) is volume, and \(T\) is temperature measured in Kelvin.

With these relationships, you can identify how one variable affects another while the quantity of gas remains constant. For example, if you increase the temperature of a gas while maintaining its pressure, the gas will expand, increasing its volume. Conversely, if the temperature decreases, so will the volume. Understanding these principles helps solve many practical problems in chemistry and physics.

Volume Calculations

When calculating the volume of a gas under changing conditions, the Combined Gas Law is indispensable. This exercise involves finding the new volume of oxygen gas when its temperature and pressure change to Standard Temperature and Pressure (STP).

To perform such calculations:

• First, convert all temperatures to Kelvin by adding 273.15 to the Celsius value.
• Next, plug the known values into the Combined Gas Law formula.
• Finally, solve for the unknown variable, usually the final volume \(V_2\).

These steps ensure you accurately determine how volume changes with varying conditions. In our exercise, you might notice that changing both pressure and temperature to standard conditions requires adjustment and precision. Solving real-world problems like these equips you with a practical understanding of the behavior of gases.

STP Conditions

In chemistry, STP stands for Standard Temperature and Pressure. It serves as a reference point to simplify the comparison of gases under uniform conditions. STP is defined as a temperature of 273.15 Kelvin (0°C) and a pressure of 1 atmosphere (atm). This standardized measurement system helps scientists and students to consistently work with gases without the confusion of varying conditions.

STP is particularly useful in calculations involving gas volumes. Using STP allows for easier conversion and comparison of gas volumes, especially in chemical reactions where stoichiometry calculations are involved. At STP, one mole of any ideal gas occupies a volume of 22.4 liters.

In the exercise, converting to STP conditions provided a straightforward way to evaluate and solve for the final volume. This standardization proves crucial, as it eliminates variables and uncertainties that can occur when conditions change. Understanding STP conditions is a key part of mastering topics involving gases and their behavior.