Question

Home Fuel Propane \(\left(C_{3} H_{8}\right)\) is a gas commonly used as a home fuel for cooking and heating. a. Calculate the volume that 0.540 mol of propane occupies at STP. b. Think about the size of this volume and the amount of propane that it contains. Why do you think propane is usually liquefied before it is transported?

Short answer

0.540 mol of propane occupies 12.075 L at STP. Propane is usually liquefied before transportation because it significantly reduces its volume, making it easier to transport and store. Liquid propane is denser, requires less pressurized containers, and has a higher energy content, making it a more efficient means of storing and using fuel.

Step-by-step solution

a. Calculate the volume

For this part, we have to calculate the volume occupied by 0.540 mol of propane at STP. We will use the ideal gas equation: PV = nRT. Temperature (T) = 273.15 K Pressure (P) = 1 atm Number of moles (n) = 0.540 mol Gas constant (R) = 0.0821 \(\frac{L·atm}{K·mol}\) Rearranging the equation for the volume (V) gives us: V = \(\frac{nRT}{P}\) Now, we can substitute the values and calculate the volume: V = \(\frac{0.540 \times 0.0821 \times 273.15}{1}\) V = 12.075 L So, 0.540 mol of propane occupies 12.075 L at STP.

b. The reason for liquefying propane for transportation

The calculated volume of 0.540 mol of propane at STP is 12.075 L. If we think about it, this volume is quite large considering the amount of propane, making it impractical to transport and store as a gas. Liquefying propane involves compressing and cooling it, which significantly reduces its volume. As a result, propane in its liquid form offers several advantages for transportation: 1. Reduced volume makes it easier to transport and store, especially in large quantities. 2. Liquid propane is much denser than the gaseous form, which means it takes up less space and can be efficiently transported over long distances. 3. It also requires less pressurized containers in comparison to the gaseous or compressed form. 4. Finally, the energy content of liquid propane is high, making it a more efficient means of storing and using fuel for various applications. These reasons justify why propane is usually liquefied before it is transported.

Key concepts

STP Conditions

STP stands for Standard Temperature and Pressure, which are specific conditions used to make calculations with gases more straightforward. At STP, the temperature is set at 273.15 Kelvin (which is equivalent to 0 degrees Celsius), and the pressure is 1 atmosphere (atm).
These conditions are particularly handy when using the ideal gas law, which is a common equation used in chemistry to link the pressure, volume, temperature, and number of moles of a gas. By using STP, calculations and comparisons between different gases become more standardized and predictable.
STP conditions simplify the interaction of gases in reactions and calculations, as you'll always know what to expect from gases measured under these conditions. This predictability is essential in scientific experiments and industrial applications involving gases.

Propane Gas Calculations

When working with propane gas at STP, the ideal gas law becomes an essential tool. The equation is given as: \[ PV = nRT \] where \( P \) is the pressure, \( V \) is the volume, \( n \) stands for the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/(K·mol)), and \( T \) is the temperature.
For propane, if we know the number of moles and use the STP conditions, we can easily find the volume it occupies. For instance, if you have 0.540 moles of propane, the corresponding volume at STP can be calculated by rearranging the formula to isolate \( V \). With known values, you can solve to find the volume, which comes out to be approximately 12.075 liters.
This straightforward calculation illustrates the usefulness of the ideal gas law in determining how much space a given amount of gas occupies under standard conditions.

Liquefaction of Gases

Liquefaction refers to the process of turning gas into a liquid state, typically by cooling and compressing it. For propane, liquefaction is particularly advantageous, especially for storage and transportation.
When propane is liquefied, it condenses from a gas that takes up a large volume into a much denser liquid. This drastically reduces the volume the propane occupies. For example, the 12.075 liters for 0.540 moles of propane as a gas can be reduced substantially when turned into a liquid.
The compactness of liquefied gases leads to easier storage and transportation. Liquefied propane requires less space, which is crucial for efficient fuel storage solutions and logistics. It allows for significant amounts of energy to be stored in smaller containers, making it ideal for domestic and industrial usage.

Gas Transportation

Transporting gases like propane requires careful planning due to their volume in gaseous form. By liquefying gases, the process becomes more manageable. Transporting propane in its liquid state allows for the carriage of larger quantities in a single shipment, as opposed to its gaseous form.
Liquefied propane can be transported in specialized containers that are designed to keep the gas in its liquid state, which minimizes space usage and maximizes efficiency. This also reduces the need for high-pressure containers, adding to safety measures.
As liquid propane is much denser, not only does it occupy less space, but it also stores more energy, making it an efficient means for fuel supply chains. This efficiency in transportation plays a significant role in meeting energy demands, contributing to its popularity as a reliable energy source.