Question

What is the volume occupied by \(1.00 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) gas at STP?

Short answer

The volume occupied by 1.00 mol of H2 gas at STP is 22.4 liters.

Step-by-step solution

The standard conditions

Define the standard temperature and pressure (STP) conditions. STP is a temperature of 273.15 Kelvin (0 degrees Celsius) and a pressure of 1 atmosphere.

Defining the volume of gas at STP

Recall the convention that one mole of any gas, under STP conditions, occupies 22.4 liters. This is a standard rule in chemistry and needs to be remembered.

Application to the exercise

Use the definition from step 2 to answer the exercise. As we are asked for the volume occupied by 1.00 mol of H2 gas at STP, we know from Step 2 that this is 22.4 liters. Therefore, 1.00 mol of H2 gas at STP occupies 22.4 liters.

Key concepts

Standard Temperature and Pressure

Understanding the concept of Standard Temperature and Pressure (STP) is fundamental in chemistry, especially when studying gases. STP is defined as a temperature of 273.15 Kelvin (0°C) and a pressure of 1 atmosphere (atm). These conditions are agreed upon as a reference point, to provide a standard for comparing the properties of gases.

At STP, gases have their particles spread out to an extent that balances the two conditions, making it easier to predict and compare their behavior. For instance, when you're told that a gas is measured at STP, you can immediately infer several properties about that gas without further information. It's important to note that the defined temperature is actually the freezing point of water, and 1 atmosphere is approximately the pressure at sea level.

When dealing with problems involving gases, always check if the conditions are at STP, as this can simplify calculations significantly. Studies of gases under standard conditions allow scientists and educators to draw comparisons and understand the behavior of different substances more easily.

Molar Volume of Gas

The molar volume of a gas refers to the volume that one mole of a gas occupies at a specific temperature and pressure. In the context of STP, one mole of any gas occupies 22.4 liters - a figure that is essential in performing stoichiometric calculations in chemistry.

Why exactly 22.4 liters? This volume is derived from the ideal gas law combined with Avogadro's hypothesis. It represents the volume that Avogadro's number of particles, or one mole, will occupy when the particles are free to move but also slightly attracted or repelled by each other, just as they would be under the conditions of STP.

To use the molar volume in calculations, you need to remember that this value is exact only at STP. If the temperature or pressure differs, the volume will change. Molar volume is also used to derive other important quantities, such as gas density and molar mass, and can be crucial when converting between the mass of a gas and the volume it occupies.

Avogadro's Law

Avogadro's Law is a principle that establishes a direct relationship between the volume of a gas and the number of moles of gas present when the temperature and pressure are held constant. It states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules.

This law implies that the volume of a gas is proportional to the number of moles as long as the temperature and pressure are consistent. For example, if you have a certain volume of hydrogen gas and double the amount while keeping temperature and pressure steady, the volume will also double. This direct proportionality is written mathematically as: \( V \propto n \) where \(V\) represents volume and \(n\) is the number of moles.

The significance of Avogadro's Law can't be overstated. It's the very reason why we can use the molar volume of gas at STP. It links the microscopic, particle-level view of gases to the macroscopic level that we can measure and observe in the laboratory. Understanding this conceptually simple, yet profound, law is key to mastering many chemistry problems involving gases.