Question

What volume does 35 moles of \(\mathrm{N}_{2}\) occupy at STP?

Short answer

35 moles of N₂ gas occupies a volume of approximately 938.67 liters at STP, calculated using the Ideal Gas Law equation: \(V = \frac{nRT}{P}\).

Step-by-step solution

Write down the Ideal Gas Law equation

We'll start by writing down the Ideal Gas Law equation: PV = nRT.

Identify the given values

We have the following values: - Pressure (P) at STP = 1 atm - Temperature (T) at STP = 273.15 K - Number of moles (n) = 35 moles - Ideal Gas Constant (R) = 0.082 L atm/K mol

Rearrange the Ideal Gas Law equation to solve for Volume (V)

We need to find the volume (V), so we can rearrange the Ideal Gas Law equation to isolate V: V = nRT / P

Plug in the known values and calculate the volume

Now, we can plug in the known values into the equation: V = (35 moles) × (0.082 L atm/K mol) × (273.15 K) / (1 atm) Calculate the result: V ≈ 938.67 L So, 35 moles of N₂ gas occupies a volume of approximately 938.67 liters at STP.

Key concepts

STP (Standard Temperature and Pressure)

Understanding Standard Temperature and Pressure (STP) is crucial for studying and working with gases. STP is a reference point used in chemistry to denote a specific set of conditions—namely, a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). These conditions are significant because they allow for the standardization of comparisons and calculations involving gases.
At STP, gases have predictable behavior, which can be applied to the Ideal Gas Law for various calculations, like determining the volume of a gas. For instance, it's important to know that at STP, one mole of any ideal gas occupies 22.4 liters (the molar volume of an ideal gas at STP), a figure derived from experimental observations. This fact simplifies many calculations and is a key piece of knowledge for any student learning about gas properties. When solving problems involving gases at STP, ensure to use these standardized conditions for temperature and pressure to obtain accurate and comparable results.

Molar Volume of Gas

The molar volume of a gas is the volume one mole of the gas occupies under specified conditions, commonly at STP. Since gases are highly compressible and expand to fill their containers, their volume can vary widely with temperature and pressure changes. However, the molar volume at STP is a constant 22.4 L/mol for any ideal gas.
Understanding this concept is vital for performing calculations related to the quantity of gas. It provides a base for deducing the quantity or volume of gas without going through complex calculations every time. For example, if you know you have 2 moles of hydrogen gas at STP, you can simply multiply the number of moles by the molar volume (2 mol × 22.4 L/mol) to find that the hydrogen occupies 44.8 liters. This simplification is an essential tool for students and professionals alike when they are involved with stoichiometry and gas law calculations.

Gas Law Calculations

Calculating various properties of gases is a routine but fundamental aspect of chemistry, and for this, understanding the gas laws is imperative. The Ideal Gas Law, expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, is the equation that ties together these properties.
To solve for any one variable, you simply need the other variables. When rearranging the equation to solve for volume (V = nRT / P), as seen in the provided exercise, you can substitute known values to find the unknown. Always pay attention to units, as standardizing units, such as temperature in Kelvin and pressure in atmospheres, is crucial for obtaining correct results.

Practical Application

Suppose you have a certain number of moles of a gas and need to find out what volume it would occupy under a new set of conditions. By applying the Ideal Gas Law and solving for V, you can predict the new volume. It's a straightforward application but essential, whether you're measuring gas in a laboratory or calculating reactions for industrial processes. In the classroom, mastering these calculations is not just about solving textbook problems but also about preparing for real-life applications where understanding the behavior of gases is critical.